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Properties

Label 1175.4.s
Level $1175$
Weight $4$
Character orbit 1175.s
Rep. character $\chi_{1175}(6,\cdot)$
Character field $\Q(\zeta_{115})$
Dimension $31504$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1175 = 5^{2} \cdot 47 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1175.s (of order \(115\) and degree \(88\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1175 \)
Character field: \(\Q(\zeta_{115})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1175, [\chi])\).

Total New Old
Modular forms 31856 31856 0
Cusp forms 31504 31504 0
Eisenstein series 352 352 0

Trace form

\( 31504 q - 63 q^{2} - 55 q^{3} + 1361 q^{4} - 44 q^{5} - 95 q^{6} - 176 q^{7} - 221 q^{8} + 3059 q^{9} + O(q^{10}) \) \( 31504 q - 63 q^{2} - 55 q^{3} + 1361 q^{4} - 44 q^{5} - 95 q^{6} - 176 q^{7} - 221 q^{8} + 3059 q^{9} - 22 q^{10} + 109 q^{11} - 347 q^{12} - 63 q^{13} - 147 q^{14} - 214 q^{15} + 5753 q^{16} + 129 q^{17} - 308 q^{18} + 89 q^{19} - 402 q^{20} + 99 q^{21} - 527 q^{22} - 727 q^{23} - 564 q^{24} - 708 q^{25} - 1448 q^{26} - 535 q^{27} - 475 q^{28} + 237 q^{29} - 332 q^{30} + 381 q^{31} + 216 q^{32} - 115 q^{33} - 95 q^{34} - 6176 q^{35} + 22901 q^{36} + 129 q^{37} + 2483 q^{38} + 453 q^{39} - 3500 q^{40} + 3617 q^{41} + 1781 q^{42} + 1232 q^{43} - 1165 q^{44} - 5236 q^{45} - 8260 q^{46} - 2388 q^{47} - 2848 q^{48} - 67504 q^{49} - 7030 q^{50} - 6912 q^{51} - 4465 q^{52} + 2057 q^{53} - 1901 q^{54} - 1168 q^{55} - 13809 q^{56} + 1548 q^{57} - 3233 q^{58} + 1341 q^{59} - 45516 q^{60} + 5961 q^{61} + 3293 q^{62} + 2427 q^{63} + 28243 q^{64} - 1298 q^{65} - 3643 q^{66} + 6129 q^{67} - 3988 q^{68} - 2347 q^{69} + 2370 q^{70} + 1873 q^{71} - 8131 q^{72} - 3855 q^{73} - 200 q^{74} - 4454 q^{75} - 3476 q^{76} + 819 q^{77} + 10503 q^{78} - 1231 q^{79} - 2595 q^{80} + 30763 q^{81} + 11732 q^{82} + 3633 q^{83} + 5219 q^{84} + 2638 q^{85} + 1705 q^{86} - 819 q^{87} + 10729 q^{88} + 97 q^{89} - 16648 q^{90} - 821 q^{91} + 19987 q^{92} - 4204 q^{93} - 25784 q^{94} - 20930 q^{95} - 14967 q^{96} - 2367 q^{97} - 9937 q^{98} - 15656 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1175, [\chi])\) into newform subspaces

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