-
hmf_forms • Show schema
{'deg': 3, 'dimension': 21, 'disc': 1304, 'field_bad_primes': [2, 163], 'field_label': '3.3.1304.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '3.3.1304.1-11.1-d', 'label_nsuffix': 3, 'label_suffix': 'd', 'level_bad_primes': [11], 'level_ideal': '[11, 11, 2*w^2 - 21]', 'level_label': '11.1', 'level_norm': 11, 'parallel_weight': 2, 'short_label': '11.1-d', 'weight': '[2, 2, 2]'} -
hmf_hecke • Show schema
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4*x^20 - 26*x^19 + 117*x^18 + 262*x^17 - 1424*x^16 - 1207*x^15 + 9346*x^14 + 1647*x^13 - 35805*x^12 + 7253*x^11 + 80968*x^10 - 34722*x^9 - 104417*x^8 + 58458*x^7 + 70925*x^6 - 44286*x^5 - 21774*x^4 + 14244*x^3 + 1676*x^2 - 1344*x + 128', 'label': '3.3.1304.1-11.1-d'} -
hmf_fields • Show schema
{'degree': 3, 'discriminant': 1304, 'ideals': ['[1, 1, 1]', '[2, 2, -w]', '[2, 2, -1/2*w^2 + 3/2*w]', '[3, 3, -w^2 + 3*w + 1]', '[4, 2, 1/2*w^2 - 1/2*w - 7]', '[4, 2, -w^2 + 11]', '[4, 4, 3/2*w^2 - 1/2*w - 17]', '[6, 6, -w^2 + 10]', '[6, 6, -1/2*w^2 - 1/2*w + 4]', '[8, 2, 2]', '[8, 4, -1/2*w^2 + 1/2*w + 5]', '[8, 4, w + 1]', '[8, 8, 1/2*w^2 + 1/2*w - 3]', '[9, 3, w^2 + w - 7]', '[9, 9, 1/2*w^2 - 1/2*w - 6]', '[11, 11, 2*w^2 - 21]', '[12, 6, 1/2*w^2 - 1/2*w - 3]', '[12, 6, w - 1]', '[12, 12, w + 2]', '[16, 4, -2*w]', '[16, 4, -w^2 + 3*w]', '[16, 4, w^2 - 4*w - 1]', '[16, 8, -1/2*w^2 + 1/2*w + 1]', '[16, 16, -w + 2]', '[17, 17, -1/2*w^2 + 5/2*w]', '[18, 6, -1/2*w^2 - 1/2*w + 5]', '[18, 6, -1/2*w^2 - 1/2*w + 2]', '[18, 18, -1/2*w^2 + 3/2*w + 2]', '[18, 18, 1/2*w^2 + 1/2*w - 1]', '[19, 19, -1/2*w^2 + 1/2*w + 2]', '[22, 22, -w - 4]', '[22, 22, -1/2*w^2 - 1/2*w + 6]', '[24, 6, -2*w^2 + 6*w + 2]', '[24, 12, 1/2*w^2 - 5/2*w - 1]', '[24, 12, 2*w^2 - 7*w - 1]', '[24, 24, -1/2*w^2 + 3/2*w - 1]', '[27, 3, 3]', '[27, 27, 2*w + 1]', '[32, 4, w^2 - w - 14]', '[32, 4, -2*w^2 + 22]', '[32, 8, -w^2 + 9]', '[32, 8, 3*w^2 - w - 34]', '[32, 16, -5/2*w^2 + 17/2*w + 1]', '[32, 32, w^2 - 2*w]', '[33, 33, -1/2*w^2 - 3/2*w + 2]', '[34, 34, 3/2*w^2 + 3/2*w - 11]', '[34, 34, -3/2*w^2 + 1/2*w + 18]', '[36, 6, -1/2*w^2 + 5/2*w - 1]', '[36, 6, w^2 - 2*w - 1]', '[36, 12, 1/2*w^2 + 1/2*w + 1]', '[36, 18, -w^2 + 2*w + 17]', '[36, 18, -3/2*w^2 + 7/2*w + 1]', '[36, 36, w^2 - 4*w]', '[37, 37, w^2 - w - 13]', '[37, 37, -1/2*w^2 + 1/2*w + 8]', '[37, 37, 5/2*w^2 - 17/2*w - 2]', '[38, 38, -1/2*w^2 + 7/2*w + 1]', '[38, 38, 5/2*w^2 - 15/2*w - 2]', '[44, 22, 1/2*w^2 - 1/2*w + 1]', '[44, 22, -w^2 + 4*w - 1]', '[44, 44, -1/2*w^2 + 3/2*w + 3]', '[47, 47, -3/2*w^2 + 11/2*w]', '[48, 12, -2*w^2 + 20]', '[48, 12, -w^2 - w + 8]', '[48, 12, w^2 - 13]', '[48, 24, -9/2*w^2 + 1/2*w + 49]', '[48, 48, 5/2*w^2 - 3/2*w - 31]', '[51, 51, 2*w + 7]', '[53, 53, w^2 - w - 7]', '[54, 6, 3*w]', '[54, 6, 3/2*w^2 - 9/2*w]', '[54, 54, -5/2*w^2 + 15/2*w + 1]', '[54, 54, 5/2*w^2 + 1/2*w - 24]', '[57, 57, 2*w^2 - 2*w - 27]', '[59, 59, 2*w - 1]', '[61, 61, -3/2*w^2 + 3/2*w + 20]', '[64, 4, 4]', '[64, 8, -w^2 + w + 10]', '[64, 8, 2*w + 2]', '[64, 8, w^2 - 2*w - 3]', '[64, 16, w^2 + w - 6]', '[64, 32, 3/2*w^2 + 1/2*w - 15]', '[64, 64, 7/2*w^2 - 1/2*w - 37]', '[66, 66, w^2 - 2*w - 2]', '[66, 66, -1/2*w^2 + 7/2*w]', '[67, 67, w^2 - 3*w - 3]', '[68, 34, -1/2*w^2 - 3/2*w + 3]', '[68, 34, w - 5]', '[68, 68, -w^2 + 8]', '[71, 71, w^2 - w - 1]', '[72, 6, 2*w^2 + 2*w - 14]', '[72, 12, 7/2*w^2 + 1/2*w - 35]', '[72, 12, -2*w^2 + w + 23]', '[72, 18, w^2 - w - 12]', '[72, 24, 2*w^2 - 7*w - 2]', '[72, 36, -w - 5]', '[72, 36, 5/2*w^2 - 1/2*w - 29]', '[72, 72, -2*w^2 - w + 18]', '[73, 73, 3*w^2 - w - 33]', '[74, 74, -1/2*w^2 - 1/2*w + 9]', '[74, 74, -1/2*w^2 + 3/2*w - 2]', '[74, 74, -3/2*w^2 + 1/2*w + 14]', '[74, 74, -1/2*w^2 + 3/2*w + 4]', '[74, 74, -1/2*w^2 - 5/2*w + 1]', '[74, 74, 1/2*w^2 - 3/2*w - 9]', '[76, 38, 3/2*w^2 + 1/2*w - 13]', '[76, 38, w^2 + 2*w - 5]', '[76, 76, 3*w^2 - 32]', '[79, 79, w^2 - w - 11]', '[79, 79, w^2 - 3*w + 1]', '[79, 79, -2*w - 5]', '[81, 9, 1/2*w^2 - 5/2*w - 2]', '[81, 9, 3*w^2 - 9*w - 3]', '[81, 81, -3*w^2 + w + 35]', '[88, 22, 4*w^2 - 42]', '[88, 44, 7/2*w^2 - 23/2*w - 3]', '[88, 44, 2*w^2 + w - 17]', '[88, 88, -3/2*w^2 + 5/2*w + 1]', '[89, 89, -2*w - 3]', '[94, 94, 5/2*w^2 + 1/2*w - 25]', '[94, 94, 3/2*w^2 + 3/2*w - 10]', '[96, 12, w^2 - w - 6]', '[96, 12, 2*w - 2]', '[96, 24, 2*w + 4]', '[96, 24, w^2 - 1]', '[96, 48, -1/2*w^2 + 1/2*w + 9]', '[96, 96, -2*w^2 + w + 22]', '[99, 33, -w^2 - w + 1]', '[99, 99, -3/2*w^2 + 11/2*w + 2]', '[101, 101, w^2 + w - 9]', '[101, 101, 3/2*w^2 + 1/2*w - 16]', '[101, 101, -3/2*w^2 + 7/2*w]', '[102, 102, -1/2*w^2 - 1/2*w - 2]', '[102, 102, 1/2*w^2 - 3/2*w - 5]', '[106, 106, w^2 - 4*w - 2]', '[106, 106, -7/2*w^2 + 21/2*w + 4]', '[107, 107, 1/2*w^2 + 3/2*w - 4]', '[108, 6, -3/2*w^2 + 3/2*w + 21]', '[108, 6, 3*w^2 - 33]', '[108, 12, -9/2*w^2 + 3/2*w + 51]', '[108, 54, -3/2*w^2 - 1/2*w + 17]', '[108, 54, -w^2 + 7]', '[108, 108, 1/2*w^2 - 3/2*w - 11]', '[111, 111, 2*w - 5]', '[111, 111, -w^2 - w + 5]', '[111, 111, -3/2*w^2 + 7/2*w + 4]', '[113, 113, -1/2*w^2 + 1/2*w - 2]', '[113, 113, -4*w^2 + 41]', '[113, 113, 3/2*w^2 - 7/2*w - 2]', '[114, 114, -3/2*w^2 + 1/2*w + 19]', '[114, 114, -1/2*w^2 + 3/2*w + 8]', '[118, 118, 7/2*w^2 - 25/2*w - 2]', '[118, 118, -2*w^2 + w]', '[121, 11, 2*w^2 - 8*w - 1]', '[121, 121, -2*w + 3]', '[122, 122, w^2 - 14]', '[122, 122, 1/2*w^2 - 3/2*w - 6]', '[125, 5, -5]', '[128, 8, -4*w]', '[128, 8, -2*w^2 + 6*w]', '[128, 8, 2*w^2 - 8*w - 2]', '[128, 16, 3*w^2 + 2*w - 25]', '[128, 16, -w^2 + w + 2]', '[128, 32, -2*w + 4]', '[128, 64, -1/2*w^2 - 3/2*w - 3]', '[128, 128, 1/2*w^2 - 3/2*w - 7]', '[131, 131, 7/2*w^2 + 9/2*w - 22]', '[131, 131, -3*w^2 + 3*w + 41]', '[131, 131, w^2 - w - 5]', '[132, 66, -11/2*w^2 + 3/2*w + 61]', '[132, 66, -2*w^2 + w + 25]', '[132, 132, 4*w^2 + w - 38]', '[134, 134, 3/2*w^2 - 5/2*w - 24]', '[134, 134, 5*w^2 - 2*w - 58]', '[136, 34, -w^2 + 5*w]', '[136, 68, 3/2*w^2 - 7/2*w - 3]', '[136, 68, 2*w^2 - 3*w - 1]', '[136, 136, 3*w + 2]', '[137, 137, 3*w^2 - 9*w - 1]', '[139, 139, 2*w^2 - 19]', '[141, 141, -w^2 + w + 15]', '[142, 142, -13/2*w^2 + 3/2*w + 73]', '[142, 142, -5/2*w^2 + 3/2*w + 30]', '[144, 12, -w^2 - w + 10]', '[144, 12, -w^2 - w + 4]', '[144, 12, w^2 - 2*w - 7]', '[144, 24, -5/2*w^2 + 1/2*w + 25]', '[144, 36, -w^2 + 3*w + 4]', '[144, 36, w^2 - 2*w + 1]', '[144, 36, w^2 + w - 2]', '[144, 48, w^2 - 2*w - 16]', '[144, 72, 1/2*w^2 + 3/2*w - 5]', '[144, 144, 3/2*w^2 - 1/2*w - 13]', '[146, 146, 1/2*w^2 + 5/2*w - 2]', '[146, 146, w^2 - 6]', '[148, 74, -8*w^2 + w + 87]', '[148, 74, w^2 + 1]', '[148, 74, -3/2*w^2 + 3/2*w + 1]', '[148, 74, 3*w^2 - 10*w - 3]', '[148, 74, -3/2*w^2 + 15/2*w + 1]', '[148, 74, -1/2*w^2 + 5/2*w + 3]', '[148, 148, 1/2*w^2 - 7/2*w + 1]', '[148, 148, 2*w^2 - 5*w - 2]', '[148, 148, -w + 6]', '[151, 151, 3/2*w^2 - 3/2*w - 14]', '[152, 38, -w^2 + w + 4]', '[152, 76, -1/2*w^2 - 3/2*w + 9]', '[152, 76, -3*w + 1]', '[152, 152, -w - 6]', '[153, 51, w^2 + w - 13]', '[153, 153, -w^2 + w + 3]', '[157, 157, 1/2*w^2 + 3/2*w - 12]', '[157, 157, 11/2*w^2 - 3/2*w - 60]', '[157, 157, -1/2*w^2 + 9/2*w]', '[158, 158, -3/2*w^2 + 9/2*w + 4]', '[158, 158, -3*w^2 + 2*w + 38]', '[158, 158, 2*w^2 + 5*w]', '[158, 158, w^2 - 2]', '[158, 158, 11/2*w^2 - 1/2*w - 60]', '[158, 158, -1/2*w^2 + 7/2*w + 2]', '[159, 159, -6*w^2 + 20*w + 1]', '[162, 18, 5*w^2 - 16*w - 2]', '[162, 18, 3*w^2 - 30]', '[162, 18, -11/2*w^2 + 1/2*w + 58]', '[162, 18, 3/2*w^2 + 3/2*w - 12]', '[162, 162, -w^2 - 2*w + 6]', '[162, 162, 1/2*w^2 + 1/2*w - 10]', '[163, 163, -w^2 + w - 1]', '[163, 163, 7/2*w^2 + 5/2*w - 28]', '[167, 167, 3/2*w^2 + 1/2*w - 12]', '[171, 57, 1/2*w^2 - 5/2*w - 14]', '[171, 171, w^2 + w - 11]', '[173, 173, 1/2*w^2 + 3/2*w - 6]', '[176, 44, -2*w - 8]', '[176, 44, -w^2 + 5]', '[176, 44, -w^2 - w + 12]', '[176, 88, 3/2*w^2 - 3/2*w - 19]', '[176, 176, 4*w^2 - w - 46]', '[177, 177, 7*w^2 - 23*w - 5]', '[178, 178, 2*w^2 + 3*w]', '[178, 178, -3/2*w^2 + 13/2*w + 2]', '[183, 183, -1/2*w^2 - 3/2*w + 8]', '[187, 187, -1/2*w^2 + 1/2*w + 10]', '[188, 94, -1/2*w^2 - 3/2*w + 7]', '[188, 94, -w^2 + 3]', '[188, 188, -1/2*w^2 - 5/2*w - 5]', '[192, 12, -4*w^2 + 12*w + 4]', '[192, 24, w^2 - 5*w - 2]', '[192, 24, 4*w^2 - 14*w - 2]', '[192, 24, -3*w^2 + 2*w + 37]', '[192, 48, -w^2 + 3*w - 2]', '[192, 96, -1/2*w^2 - 7/2*w + 1]', '[192, 192, -w^2 + 4]', '[193, 193, 2*w^2 - 25]', '[197, 197, -5*w^2 - w + 49]', '[198, 66, -5/2*w^2 + 19/2*w + 1]', '[198, 66, 7/2*w^2 - 5/2*w - 44]', '[198, 198, 7/2*w^2 - 1/2*w - 36]', '[198, 198, -3/2*w^2 + 5/2*w + 23]', '[199, 199, 5/2*w^2 - 1/2*w - 30]', '[201, 201, -7/2*w^2 - 1/2*w + 34]', '[202, 202, 1/2*w^2 - 7/2*w + 2]', '[202, 202, -1/2*w^2 - 9/2*w - 2]', '[202, 202, -5/2*w^2 - 1/2*w + 26]', '[202, 202, -w^2 - 2*w - 2]', '[202, 202, -1/2*w^2 - 1/2*w - 3]', '[202, 202, -6*w^2 + w + 64]', '[204, 102, 3*w^2 - 8*w - 1]', '[204, 102, -5/2*w^2 + 17/2*w + 3]', '[204, 204, 3/2*w^2 - 1/2*w - 1]', '[209, 209, 7/2*w^2 - 3/2*w - 40]', '[211, 211, 4*w^2 - 45]', '[212, 106, -9/2*w^2 + 1/2*w + 47]', '[212, 106, 7*w^2 - 2*w - 75]', '[212, 212, -21/2*w^2 + 3/2*w + 115]', '[213, 213, 4*w^2 - 43]', '[214, 214, 3/2*w^2 - 13/2*w]', '[214, 214, -3/2*w^2 - 3/2*w - 1]', '[216, 6, 6]', '[216, 12, 3/2*w^2 - 3/2*w - 15]', '[216, 12, -3*w - 3]', '[216, 24, -3/2*w^2 - 3/2*w + 9]', '[216, 54, 4*w + 2]', '[216, 108, 1/2*w^2 - 1/2*w + 3]', '[216, 108, 2*w^2 - 5*w - 3]', '[216, 216, -w^2 + 2*w + 8]', '[219, 219, -1/2*w^2 + 5/2*w + 4]', '[222, 222, 3/2*w^2 - 17/2*w - 2]', '[222, 222, -1/2*w^2 + 7/2*w - 3]', '[222, 222, -7/2*w^2 - 3/2*w + 32]', '[222, 222, -2*w^2 + 5*w]', '[222, 222, 3/2*w^2 - 5/2*w - 2]', '[222, 222, -7/2*w^2 + 25/2*w + 3]', '[223, 223, -3/2*w^2 + 15/2*w + 2]', '[226, 226, 9/2*w^2 - 27/2*w - 2]', '[226, 226, 5/2*w^2 + 1/2*w - 29]', '[226, 226, 5/2*w^2 + 9/2*w - 12]', '[226, 226, -1/2*w^2 + 15/2*w + 1]', '[226, 226, 3/2*w^2 - 1/2*w - 12]', '[226, 226, 7/2*w^2 + 3/2*w - 31]', '[228, 114, -1/2*w^2 + 5/2*w - 5]', '[228, 114, w^2 - 4*w - 3]', '[228, 228, -1/2*w^2 - 5/2*w + 3]', '[229, 229, -7/2*w^2 + 3/2*w + 42]', '[229, 229, 3/2*w^2 - 3/2*w - 10]', '[229, 229, 2*w^2 - 2*w - 1]', '[233, 233, 13/2*w^2 - 1/2*w - 70]', '[236, 118, w^2 - 15]', '[236, 118, -3/2*w^2 - 5/2*w + 9]', '[236, 236, -5/2*w^2 - 1/2*w + 23]', '[237, 237, 5/2*w^2 + 3/2*w - 22]', '[237, 237, -2*w^2 + 8*w - 3]', '[237, 237, -w^2 + 5*w - 1]', '[241, 241, w^2 - 3*w - 5]', '[242, 22, 9/2*w^2 - 3/2*w - 49]', '[242, 22, 3/2*w^2 - 1/2*w - 20]', '[242, 242, -9/2*w^2 + 31/2*w + 2]', '[242, 242, 2*w^2 - 3*w]', '[243, 9, -3*w^2 - 3*w + 21]', '[243, 27, -3/2*w^2 + 3/2*w + 18]', '[243, 243, -1/2*w^2 - 3/2*w - 4]', '[244, 122, 3/2*w^2 + 1/2*w - 1]', '[244, 122, -2*w^2 + 7*w + 3]', '[244, 244, 3*w - 2]', '[250, 10, 5*w]', '[250, 10, 5/2*w^2 - 15/2*w]', '[256, 8, 2*w^2 - 2*w - 28]', '[256, 8, -4*w^2 + 44]', '[256, 16, -2*w^2 + 18]', '[256, 16, 6*w^2 - 2*w - 68]', '[256, 16, -w^2 - 2*w + 7]', '[256, 32, -5*w^2 + 17*w + 2]', '[256, 64, 2*w^2 - 4*w]', '[256, 128, -3/2*w^2 + 11/2*w + 3]', '[256, 256, w^2 - 4*w + 4]', '[257, 257, 3/2*w^2 - 3/2*w - 16]', '[262, 262, -2*w^2 - w + 16]', '[262, 262, 1/2*w^2 - 3/2*w - 12]', '[262, 262, w^2 - 6*w - 2]', '[262, 262, -3/2*w^2 - 7/2*w + 6]', '[262, 262, 5/2*w^2 - 3/2*w - 29]', '[262, 262, -9/2*w^2 + 27/2*w + 4]', '[263, 263, -5*w^2 + w + 57]', '[264, 66, -w^2 - 3*w + 4]', '[264, 132, -3/2*w^2 - 1/2*w + 11]', '[264, 132, w - 7]', '[264, 264, -5/2*w^2 - 1/2*w + 27]', '[267, 267, -3*w^2 + 11*w + 1]', '[268, 134, w + 7]', '[268, 134, -3/2*w^2 + 3/2*w + 17]', '[268, 268, -7/2*w^2 + 1/2*w + 41]', '[272, 68, 3*w^2 + 3*w - 22]', '[272, 68, -3*w^2 + w + 36]', '[272, 68, -w^2 + 2*w + 15]', '[272, 136, 11/2*w^2 + 1/2*w - 55]', '[272, 272, -7/2*w^2 + 21/2*w + 1]', '[274, 274, 13/2*w^2 - 3/2*w - 69]', '[274, 274, 5/2*w^2 + 1/2*w - 28]', '[277, 277, -3*w^2 - w + 27]', '[277, 277, 5/2*w^2 - 1/2*w - 24]', '[277, 277, -9/2*w^2 + 25/2*w + 2]', '[278, 278, -3*w - 4]', '[278, 278, -3/2*w^2 - 7/2*w - 2]', '[282, 282, -1/2*w^2 + 3/2*w - 4]', '[282, 282, -w^2 - 4*w + 2]', '[283, 283, -1/2*w^2 - 11/2*w - 2]', '[284, 142, 3/2*w^2 + 1/2*w - 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5/2*w - 13]', '[1952, 1952, 1/2*w^2 + 13/2*w + 9]', '[1954, 1954, 13/2*w^2 - 51/2*w - 4]', '[1954, 1954, -11/2*w^2 - 7/2*w - 1]', '[1956, 978, -7/2*w^2 + 15/2*w + 5]', '[1956, 978, -w^2 + 8*w + 35]', '[1956, 978, -13/2*w^2 + 9/2*w + 83]', '[1956, 978, 9*w^2 - 28*w - 11]', '[1956, 1956, -18*w^2 + 5*w + 202]', '[1956, 1956, 3/2*w^2 - 17/2*w + 7]', '[1958, 1958, 2*w^2 + 11*w + 12]', '[1958, 1958, 5/2*w^2 + 1/2*w - 16]', '[1959, 1959, 1/2*w^2 - 13/2*w - 24]', '[1961, 1961, -8*w^2 + 87]', '[1961, 1961, 11/2*w^2 - 3/2*w - 54]', '[1961, 1961, 33/2*w^2 - 109/2*w - 8]', '[1964, 982, 2*w^2 - 5*w - 13]', '[1964, 982, -5/2*w^2 - 7/2*w + 7]', '[1964, 1964, -2*w^2 - 3*w + 18]', '[1966, 1966, -3/2*w^2 - 7/2*w - 6]', '[1966, 1966, 21/2*w^2 - 71/2*w - 4]', '[1966, 1966, 15/2*w^2 - 41/2*w - 3]', '[1966, 1966, w^2 - 4*w - 14]', '[1966, 1966, -4*w^2 + 9*w]', '[1966, 1966, -13/2*w^2 - 9/2*w + 52]', '[1971, 219, -9*w^2 + 3*w + 99]', '[1971, 1971, w^2 - w - 21]', '[1973, 1973, 5*w^2 - 11*w - 1]', '[1973, 1973, 3/2*w^2 - 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7*w + 35]', '[9944, 4972, -8*w^2 + 21*w + 25]', '[9944, 4972, 3/2*w^2 + 13/2*w - 31]', '[9944, 9944, 9*w^2 + 4*w - 84]', '[9944, 9944, 12*w^2 - 25*w - 6]', '[9944, 9944, 1/2*w^2 + 9/2*w + 21]', '[9946, 9946, 3/2*w^2 - 17/2*w - 15]', '[9946, 9946, -7/2*w^2 - 7/2*w - 6]', '[9948, 4974, -21/2*w^2 - 7/2*w + 95]', '[9948, 4974, -7*w^2 - 12*w + 37]', '[9948, 9948, -22*w^2 + w + 234]', '[9949, 9949, 3/2*w^2 - 3/2*w - 34]', '[9956, 4978, -3/2*w^2 - 33/2*w - 7]', '[9956, 4978, -w^2 + 8*w + 27]', '[9956, 4978, -6*w^2 + 13*w + 9]', '[9956, 4978, -7/2*w^2 + 19/2*w - 7]', '[9956, 4978, 3*w^2 - 18*w - 7]', '[9956, 4978, -9/2*w^2 + 5/2*w + 63]', '[9956, 9956, -2*w^2 - w - 10]', '[9956, 9956, -14*w^2 + 5*w + 154]', '[9956, 9956, -5/2*w^2 - 29/2*w + 3]', '[9964, 4982, -w^2 + 6*w - 19]', '[9964, 4982, -5/2*w^2 - 19/2*w + 11]', '[9964, 9964, -9/2*w^2 - 1/2*w + 31]', '[9966, 9966, -13/2*w^2 + 31/2*w + 12]', '[9966, 9966, 5/2*w^2 - 31/2*w + 19]', '[9967, 9967, 11/2*w^2 - 31/2*w - 108]', '[9969, 9969, 25/2*w^2 - 73/2*w - 12]', '[9972, 1662, -w^2 - 4*w - 17]', '[9972, 1662, 2*w^2 - 7*w + 13]', '[9972, 1662, 7/2*w^2 - 11/2*w - 41]', '[9972, 1662, 5/2*w^2 + 23/2*w - 7]', '[9972, 1662, -13/2*w^2 + 5/2*w + 83]', '[9972, 1662, -2*w^2 + 7*w + 35]', '[9972, 3324, 8*w^2 + 11*w - 50]', '[9972, 3324, 8*w^2 - w - 98]', '[9972, 3324, 4*w^2 + w - 22]', '[9972, 4986, 5/2*w^2 + 7/2*w + 9]', '[9972, 4986, -5*w^2 + 6*w + 29]', '[9972, 4986, -2*w^2 + 13*w - 11]', '[9972, 4986, 1/2*w^2 - 17/2*w - 19]', '[9972, 4986, -9/2*w^2 + 25/2*w - 5]', '[9972, 4986, 4*w^2 - 21*w - 7]', '[9972, 9972, -2*w^2 + 7*w + 22]', '[9972, 9972, -2*w^2 - 15*w + 2]', '[9972, 9972, 5/2*w^2 - 3/2*w - 43]', '[9974, 9974, -29/2*w^2 - 1/2*w + 146]', '[9974, 9974, -23/2*w^2 + 65/2*w + 10]', '[9974, 9974, -1/2*w^2 - 5/2*w - 19]', '[9974, 9974, -33*w^2 + 4*w + 358]', '[9974, 9974, w^2 - 20*w - 6]', '[9974, 9974, -3/2*w^2 - 27/2*w - 10]', '[9977, 9977, -21*w^2 + w + 219]', '[9978, 9978, -1/2*w^2 - 21/2*w - 19]', '[9978, 9978, -9/2*w^2 + 7/2*w + 28]', '[9979, 9979, 13/2*w^2 - 1/2*w - 58]', '[9981, 3327, 4*w^2 + 4*w - 13]', '[9981, 9981, 9/2*w^2 - 29/2*w - 14]', '[9986, 9986, -9/2*w^2 + 7/2*w - 3]', '[9986, 9986, 17/2*w^2 - 63/2*w]', '[9992, 2498, 6*w^2 + 6*w - 38]', '[9992, 4996, 19/2*w^2 + 5/2*w - 95]', '[9992, 4996, 6*w^2 + 17*w - 13]', '[9992, 9992, -1/2*w^2 + 35/2*w + 63]', '[9994, 9994, -5/2*w^2 + 15/2*w + 21]', '[9994, 9994, 5/2*w^2 + 1/2*w + 8]', '[9999, 3333, -2*w^2 - 14*w - 13]', '[9999, 3333, 1/2*w^2 - 17/2*w - 20]', '[9999, 3333, 23*w^2 - 73*w - 11]', '[9999, 9999, 11/2*w^2 + 25/2*w + 6]', '[9999, 9999, 9/2*w^2 - 13/2*w - 10]', '[9999, 9999, 9*w^2 + w - 85]'], 'label': '3.3.1304.1', 'narrow_class_no': 1, 'primes': ['[2, 2, -w]', '[2, 2, -1/2*w^2 + 3/2*w]', '[3, 3, -w^2 + 3*w + 1]', '[9, 3, w^2 + w - 7]', '[11, 11, 2*w^2 - 21]', '[17, 17, -1/2*w^2 + 5/2*w]', '[19, 19, -1/2*w^2 + 1/2*w + 2]', '[37, 37, w^2 - w - 13]', '[37, 37, -1/2*w^2 + 1/2*w + 8]', '[37, 37, 5/2*w^2 - 17/2*w - 2]', '[47, 47, -3/2*w^2 + 11/2*w]', '[53, 53, w^2 - w - 7]', '[59, 59, 2*w - 1]', '[61, 61, -3/2*w^2 + 3/2*w + 20]', '[67, 67, w^2 - 3*w - 3]', '[71, 71, w^2 - w - 1]', '[73, 73, 3*w^2 - w - 33]', '[79, 79, w^2 - w - 11]', '[79, 79, w^2 - 3*w + 1]', '[79, 79, -2*w - 5]', '[89, 89, -2*w - 3]', '[101, 101, w^2 + w - 9]', '[101, 101, 3/2*w^2 + 1/2*w - 16]', '[101, 101, -3/2*w^2 + 7/2*w]', '[107, 107, 1/2*w^2 + 3/2*w - 4]', '[113, 113, -1/2*w^2 + 1/2*w - 2]', '[113, 113, -4*w^2 + 41]', '[113, 113, 3/2*w^2 - 7/2*w - 2]', '[121, 11, 2*w^2 - 8*w - 1]', '[125, 5, -5]', '[131, 131, 7/2*w^2 + 9/2*w - 22]', '[131, 131, -3*w^2 + 3*w + 41]', '[131, 131, w^2 - w - 5]', '[137, 137, 3*w^2 - 9*w - 1]', '[139, 139, 2*w^2 - 19]', '[151, 151, 3/2*w^2 - 3/2*w - 14]', '[157, 157, 1/2*w^2 + 3/2*w - 12]', '[157, 157, 11/2*w^2 - 3/2*w - 60]', '[157, 157, -1/2*w^2 + 9/2*w]', '[163, 163, -w^2 + w - 1]', '[163, 163, 7/2*w^2 + 5/2*w - 28]', '[167, 167, 3/2*w^2 + 1/2*w - 12]', '[173, 173, 1/2*w^2 + 3/2*w - 6]', '[193, 193, 2*w^2 - 25]', '[197, 197, -5*w^2 - w + 49]', '[199, 199, 5/2*w^2 - 1/2*w - 30]', '[211, 211, 4*w^2 - 45]', '[223, 223, -3/2*w^2 + 15/2*w + 2]', '[229, 229, -7/2*w^2 + 3/2*w + 42]', '[229, 229, 3/2*w^2 - 3/2*w - 10]', '[229, 229, 2*w^2 - 2*w - 1]', '[233, 233, 13/2*w^2 - 1/2*w - 70]', '[241, 241, w^2 - 3*w - 5]', '[257, 257, 3/2*w^2 - 3/2*w - 16]', '[263, 263, -5*w^2 + w + 57]', '[277, 277, -3*w^2 - w + 27]', '[277, 277, 5/2*w^2 - 1/2*w - 24]', '[277, 277, -9/2*w^2 + 25/2*w + 2]', '[283, 283, -1/2*w^2 - 11/2*w - 2]', '[289, 17, -7/2*w^2 - 1/2*w + 36]', '[317, 317, 7*w^2 - w - 79]', '[317, 317, 3/2*w^2 - 3/2*w - 2]', '[317, 317, 2*w - 9]', '[331, 331, -3*w^2 + 5*w + 47]', '[337, 337, -3/2*w^2 + 3/2*w + 22]', '[343, 7, -7]', '[349, 349, -2*w - 9]', '[349, 349, 1/2*w^2 - 5/2*w - 6]', '[349, 349, 3/2*w^2 - 7/2*w - 8]', '[353, 353, 1/2*w^2 - 13/2*w - 2]', '[359, 359, -1/2*w^2 + 1/2*w - 4]', '[361, 19, 3/2*w^2 + 1/2*w - 10]', '[367, 367, 2*w^2 - 8*w + 1]', '[373, 373, -4*w - 3]', '[383, 383, 15/2*w^2 - 3/2*w - 80]', '[397, 397, w^2 + 3*w - 5]', '[401, 401, 2*w^2 - 2*w - 19]', '[409, 409, 2*w^2 - 1]', '[409, 409, -13/2*w^2 + 1/2*w + 68]', '[409, 409, -1/2*w^2 + 5/2*w - 6]', '[421, 421, -9/2*w^2 + 5/2*w + 54]', '[433, 433, w^2 - 5*w - 27]', '[439, 439, 9*w^2 - w - 99]', '[443, 443, 2*w^2 - 4*w - 3]', '[449, 449, -5*w^2 + 3*w + 61]', '[461, 461, 3/2*w^2 - 11/2*w - 4]', '[463, 463, -7*w^2 - w + 69]', '[463, 463, -1/2*w^2 + 9/2*w - 2]', '[463, 463, -5/2*w^2 + 17/2*w + 4]', '[467, 467, -2*w^2 + 2*w + 25]', '[487, 487, 2*w^2 - 4*w - 33]', '[491, 491, 5/2*w^2 - 9/2*w - 2]', '[499, 499, -6*w^2 + 18*w + 7]', '[499, 499, 3/2*w^2 - 3/2*w - 4]', '[499, 499, 6*w^2 - 20*w - 5]', '[503, 503, w^2 - w - 17]', '[521, 521, -w^2 - w - 3]', '[547, 547, -21/2*w^2 + 5/2*w + 118]', '[547, 547, 3*w^2 - w - 37]', '[547, 547, 6*w^2 - 2*w - 65]', '[569, 569, -13/2*w^2 - 11/2*w + 50]', '[571, 571, -7/2*w^2 + 19/2*w + 4]', '[587, 587, 11/2*w^2 + 17/2*w - 30]', '[601, 601, 2*w^2 - 2*w - 13]', '[607, 607, 3/2*w^2 + 1/2*w - 4]', '[617, 617, -1/2*w^2 - 3/2*w - 6]', '[619, 619, -1/2*w^2 + 9/2*w - 6]', '[643, 643, 2*w^2 - 27]', '[647, 647, -9/2*w^2 + 33/2*w + 4]', '[653, 653, -3*w^2 + 7*w + 3]', '[659, 659, -3/2*w^2 - 1/2*w - 2]', '[661, 661, -6*w^2 + 61]', '[677, 677, 7*w^2 - 3*w - 83]', '[683, 683, 9/2*w^2 - 33/2*w - 2]', '[701, 701, -2*w^2 + 2*w - 1]', '[709, 709, w^2 - 3*w - 9]', '[719, 719, 4*w^2 - 4*w - 55]', '[719, 719, 4*w^2 - 2*w - 45]', '[719, 719, 4*w^2 - 39]', '[727, 727, -4*w - 9]', '[727, 727, -5/2*w^2 + 5/2*w + 32]', '[727, 727, 9/2*w^2 - 29/2*w]', '[733, 733, 4*w - 11]', '[743, 743, -3/2*w^2 + 3/2*w - 2]', '[761, 761, 3/2*w^2 + 5/2*w - 24]', '[769, 769, -2*w^2 + 10*w + 3]', '[773, 773, 3/2*w^2 + 5/2*w - 12]', '[787, 787, 17/2*w^2 - 5/2*w - 92]', '[787, 787, 3*w^2 + w - 35]', '[787, 787, 4*w^2 - 10*w - 1]', '[797, 797, 6*w^2 - 67]', '[809, 809, 5/2*w^2 - 21/2*w]', '[811, 811, w^2 - 9*w - 39]', '[821, 821, -2*w^2 + 6*w + 7]', '[827, 827, 6*w - 1]', '[829, 829, 3/2*w^2 - 11/2*w - 34]', '[839, 839, 5*w^2 + 3*w - 43]', '[853, 853, -4*w^2 - 6*w + 23]', '[857, 857, 3*w^2 - w - 27]', '[859, 859, 3*w^2 - 9*w + 1]', '[863, 863, -2*w - 11]', '[863, 863, 5/2*w^2 - 5/2*w - 2]', '[863, 863, 4*w + 15]', '[877, 877, -3/2*w^2 + 15/2*w - 2]', '[881, 881, -w^2 + 7*w - 1]', '[883, 883, 4*w - 5]', '[907, 907, w^2 - 3*w - 11]', '[911, 911, 5/2*w^2 + 3/2*w - 18]', '[919, 919, 2*w^2 - 2*w - 11]', '[929, 929, 11/2*w^2 + 9/2*w - 42]', '[937, 937, 1/2*w^2 + 7/2*w - 6]', '[941, 941, -9/2*w^2 + 5/2*w + 46]', '[953, 953, 11/2*w^2 - 39/2*w - 2]', '[967, 967, -13*w^2 + w + 139]', '[977, 977, 1/2*w^2 + 11/2*w - 2]', '[983, 983, 1/2*w^2 + 15/2*w + 20]', '[983, 983, 4*w - 9]', '[983, 983, 3/2*w^2 - 15/2*w + 4]', '[991, 991, 3/2*w^2 - 11/2*w - 6]', '[991, 991, w^2 - 3*w - 15]', '[991, 991, 1/2*w^2 - 1/2*w - 14]']} -
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-2, -11, 0, 1], 'conductor': 0, 'degree': 3, 'dirichlet_group': [], 'disc_abs': 1304, 'disc_rad': 326, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[2, 1], [1, 1]]], [5, [[3, 1]]], [7, [[3, 1]]], [11, [[2, 1], [1, 1]]], [13, [[3, 1]]], [17, [[2, 1], [1, 1]]], [19, [[2, 1], [1, 1]]], [23, [[3, 1]]], [29, [[3, 1]]], [31, [[3, 1]]], [37, [[1, 3]]], [41, [[3, 1]]], [43, [[3, 1]]], [47, [[2, 1], [1, 1]]], [53, [[2, 1], [1, 1]]], [59, [[2, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [9, 3], 'galois_label': '3T2', 'galt': 2, 'grd': 36.11094017053558, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.1304.1', 'local_algs': ['2.1.0.1', '2.2.3.4', '163.1.0.1', '163.2.1.2'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 163], 'rd': 10.9251111426, 'regulator': {'__RealLiteral__': 0, 'data': '11.9265379008', 'prec': 44}, 'res': {'gal': ['-8,-8,70,-36,-35,-2,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{2} a^{2} - \\frac{1}{2} a - 4 \\)', '\\( 12 a^{2} - 2 a - 131 \\)'], 'unitsGmodule': [[3, 1], [5, 1]], 'used_grh': False, 'zk': ['1', 'a', '1/2*a^2 - 1/2*a']}
Hilbert modular form data - 3.3.1304.1-11.1-d