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Properties

Label 1175.4.u
Level $1175$
Weight $4$
Character orbit 1175.u
Rep. character $\chi_{1175}(4,\cdot)$
Character field $\Q(\zeta_{230})$
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.u (of order \(230\) and degree \(88\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1175 \)
Character field: \(\Q(\zeta_{230})\)
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

\( 31504 q - 105 q^{2} - 105 q^{3} - 1487 q^{4} - 108 q^{5} - 31 q^{6} + 105 q^{8} - 3313 q^{9} + O(q^{10}) \) \( 31504 q - 105 q^{2} - 105 q^{3} - 1487 q^{4} - 108 q^{5} - 31 q^{6} + 105 q^{8} - 3313 q^{9} - 2 q^{10} - 235 q^{11} + 215 q^{12} - 105 q^{13} - 243 q^{14} + 30 q^{15} + 5385 q^{16} + 215 q^{17} + 89 q^{19} - 278 q^{20} - 225 q^{21} - 105 q^{22} - 265 q^{23} - 284 q^{24} - 836 q^{25} + 1112 q^{26} - 645 q^{27} - 745 q^{28} + 237 q^{29} - 816 q^{30} - 507 q^{31} - 105 q^{33} - 31 q^{34} - 7600 q^{35} + 1517 q^{36} - 105 q^{37} + 2385 q^{38} + 669 q^{39} + 772 q^{40} - 3743 q^{41} - 2265 q^{42} - 1101 q^{44} - 8816 q^{45} + 7996 q^{46} - 20 q^{47} + 3060 q^{48} + 68128 q^{49} - 5458 q^{50} + 6576 q^{51} - 3895 q^{52} - 1465 q^{53} - 2161 q^{54} + 2632 q^{55} + 13171 q^{56} + 8345 q^{58} + 1341 q^{59} - 47164 q^{60} - 6087 q^{61} + 4815 q^{62} - 4435 q^{63} - 15885 q^{64} + 1738 q^{65} + 1789 q^{66} - 8505 q^{67} + 1949 q^{69} - 6206 q^{70} + 481 q^{71} + 8975 q^{72} + 4455 q^{73} - 136 q^{74} - 1282 q^{75} + 2628 q^{76} - 3535 q^{77} - 6915 q^{78} - 1231 q^{79} - 29 q^{80} + 25795 q^{81} + 6815 q^{83} + 1383 q^{84} + 3474 q^{85} - 1831 q^{86} + 12295 q^{87} + 12495 q^{88} - 223 q^{89} + 32808 q^{90} + 695 q^{91} + 2245 q^{92} + 15168 q^{94} + 5782 q^{95} - 22659 q^{96} - 105 q^{97} - 13755 q^{98} - 14560 q^{99} + O(q^{100}) \)

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.