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Properties

Label 1175.4.i
Level $1175$
Weight $4$
Character orbit 1175.i
Rep. character $\chi_{1175}(189,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $1384$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1175 = 5^{2} \cdot 47 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1175.i (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1448 1384 64
Cusp forms 1432 1384 48
Eisenstein series 16 0 16

Trace form

\( 1384 q + 1392 q^{4} - 14 q^{5} - 24 q^{6} + 3150 q^{9} + O(q^{10}) \) \( 1384 q + 1392 q^{4} - 14 q^{5} - 24 q^{6} + 3150 q^{9} - 80 q^{10} + 112 q^{14} + 328 q^{15} - 5632 q^{16} + 72 q^{19} - 604 q^{20} - 120 q^{21} - 70 q^{22} - 1180 q^{24} - 446 q^{25} + 348 q^{26} - 660 q^{27} - 720 q^{28} - 556 q^{29} + 2654 q^{30} - 828 q^{31} + 2560 q^{33} + 1520 q^{34} - 784 q^{35} - 12300 q^{36} + 3010 q^{37} - 3010 q^{38} + 1744 q^{39} + 3524 q^{40} + 596 q^{41} - 1340 q^{42} + 214 q^{45} - 2136 q^{46} - 6110 q^{48} - 70608 q^{49} - 2092 q^{50} + 3264 q^{51} + 300 q^{52} - 3810 q^{53} - 1398 q^{54} - 300 q^{55} - 1344 q^{56} + 2400 q^{59} - 4096 q^{60} - 392 q^{61} + 8830 q^{62} + 8220 q^{63} + 23040 q^{64} + 4510 q^{65} + 3690 q^{66} - 3096 q^{69} - 1146 q^{70} - 5496 q^{71} - 9520 q^{72} - 2880 q^{73} - 7240 q^{74} - 2900 q^{75} + 3748 q^{76} - 4320 q^{77} - 11790 q^{78} - 388 q^{79} - 7052 q^{80} - 32482 q^{81} + 2320 q^{83} + 9936 q^{84} + 3218 q^{85} + 9556 q^{86} + 4560 q^{87} - 9310 q^{88} + 4974 q^{89} + 14598 q^{90} - 10540 q^{92} + 752 q^{94} + 3688 q^{95} - 10764 q^{96} - 10380 q^{97} + 3280 q^{98} + 2328 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{4}^{\mathrm{old}}(1175, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1175, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)