Space of modular forms of level 1014, weight 6, and Character 1014.m

• Label: 1014.6.m
• Level: $1014$
• Weight: $6$
• Character orbit: 1014.m
• Rep. character: $\chi_{1014}(79,\cdot)$
• Character field: $\Q(\zeta_{13})$
• Dimension: $1824$
• Sturm bound: $1092$

Defining parameters

Level:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1014.m (of order \(13\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 169 \)
Character field:			\(\Q(\zeta_{13})\)
Sturm bound:			\(1092\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(1014, [\chi])\).

	Total	New	Old
Modular forms	10968	1824	9144
Cusp forms	10872	1824	9048
Eisenstein series	96	0	96

Trace form

1824 * q - 8 * q^2 + 18 * q^3 - 2432 * q^4 + 44 * q^5 + 196 * q^7 - 128 * q^8 - 12312 * q^9 + 1024 * q^10 + 752 * q^11 + 288 * q^12 - 4074 * q^13 - 1760 * q^14 - 792 * q^15 - 38912 * q^16 - 444 * q^17 - 648 * q^18 - 2788 * q^19 + 704 * q^20 + 1404 * q^21 - 23232 * q^22 - 1456 * q^23 - 104408 * q^25 + 2632 * q^26 + 1458 * q^27 + 3136 * q^28 + 1332 * q^29 + 3600 * q^30 - 41152 * q^31 - 2048 * q^32 - 2952 * q^33 - 12048 * q^34 + 32704 * q^35 - 196992 * q^36 + 40496 * q^37 - 14048 * q^38 - 5922 * q^39 - 48512 * q^40 - 19492 * q^41 + 7056 * q^42 + 26624 * q^43 + 12032 * q^44 + 3564 * q^45 + 4192 * q^46 - 68632 * q^47 + 4608 * q^48 - 291128 * q^49 + 32520 * q^50 - 2484 * q^51 + 5120 * q^52 - 62634 * q^53 - 270640 * q^55 - 28160 * q^56 - 19332 * q^57 + 140576 * q^58 + 72856 * q^59 + 69696 * q^60 + 76748 * q^61 + 74784 * q^62 + 15876 * q^63 - 622592 * q^64 - 42076 * q^65 + 7488 * q^66 + 30856 * q^67 - 7104 * q^68 + 108576 * q^69 - 312352 * q^70 - 660764 * q^71 - 10368 * q^72 + 23856 * q^73 + 758216 * q^74 + 59886 * q^75 + 284032 * q^76 - 300344 * q^77 - 35856 * q^78 - 169292 * q^79 + 11264 * q^80 - 997272 * q^81 + 50512 * q^82 - 34104 * q^83 + 22464 * q^84 + 984754 * q^85 + 1220784 * q^86 + 535500 * q^87 + 30976 * q^88 + 129524 * q^89 + 82944 * q^90 + 183148 * q^91 - 23296 * q^92 - 583506 * q^93 - 67728 * q^94 + 1983880 * q^95 + 1679940 * q^97 - 89736 * q^98 + 60912 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(1014, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{6}^{\mathrm{old}}(1014, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(1014, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 2}\)