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Properties

Label 2475.4.et
Level $2475$
Weight $4$
Character orbit 2475.et
Rep. character $\chi_{2475}(34,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $7200$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2475.et (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2475, [\chi])\).

Total New Old
Modular forms 8672 7200 1472
Cusp forms 8608 7200 1408
Eisenstein series 64 0 64

Trace form

\( 7200 q - 3600 q^{4} - 16 q^{5} + 32 q^{9} + O(q^{10}) \) \( 7200 q - 3600 q^{4} - 16 q^{5} + 32 q^{9} + 88 q^{11} - 160 q^{12} - 224 q^{14} + 692 q^{15} + 14400 q^{16} - 218 q^{20} + 96 q^{21} + 28 q^{24} - 288 q^{25} + 4992 q^{26} + 660 q^{27} - 782 q^{30} - 36 q^{31} - 1080 q^{35} + 364 q^{36} + 6020 q^{38} - 1464 q^{39} + 1400 q^{42} + 1760 q^{44} + 1622 q^{45} + 1900 q^{47} + 9310 q^{48} + 176400 q^{49} + 926 q^{50} - 656 q^{51} + 2262 q^{54} + 396 q^{55} + 2688 q^{56} - 2334 q^{59} + 9332 q^{60} - 9840 q^{62} - 5320 q^{63} + 115200 q^{64} - 1368 q^{65} - 1530 q^{67} + 1448 q^{69} - 3648 q^{71} + 9520 q^{72} - 4228 q^{74} + 178 q^{75} - 11180 q^{78} - 13008 q^{80} - 3056 q^{81} + 280 q^{83} + 7816 q^{84} - 1656 q^{85} + 9000 q^{86} + 12500 q^{87} + 8224 q^{89} - 12628 q^{90} - 15520 q^{92} - 1308 q^{95} + 336 q^{96} - 220 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2475, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2475, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2475, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)