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Properties

Label 2475.4.dq
Level $2475$
Weight $4$
Character orbit 2475.dq
Rep. character $\chi_{2475}(172,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $3584$
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.dq (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 8704 3616 5088
Cusp forms 8576 3584 4992
Eisenstein series 128 32 96

Trace form

\( 3584 q + 10 q^{2} - 10 q^{4} - 10 q^{5} - 10 q^{7} + 10 q^{8} + O(q^{10}) \) \( 3584 q + 10 q^{2} - 10 q^{4} - 10 q^{5} - 10 q^{7} + 10 q^{8} + 360 q^{10} + 6 q^{11} + 230 q^{13} + 10 q^{14} + 14142 q^{16} + 330 q^{17} + 110 q^{19} - 1076 q^{20} - 898 q^{22} - 36 q^{23} + 218 q^{25} + 12 q^{26} + 1030 q^{28} + 10 q^{29} - 12 q^{31} - 20 q^{34} + 10 q^{35} - 174 q^{37} + 1042 q^{38} - 10 q^{40} + 1740 q^{43} + 650 q^{44} - 10 q^{46} - 790 q^{47} - 3060 q^{49} - 2470 q^{50} + 4670 q^{52} - 118 q^{53} + 610 q^{55} - 116 q^{56} + 1758 q^{58} + 1030 q^{59} - 10 q^{61} - 4460 q^{62} - 6930 q^{64} - 380 q^{65} - 1724 q^{67} + 8020 q^{68} + 670 q^{70} + 1252 q^{71} + 230 q^{73} + 5390 q^{74} + 4068 q^{77} - 10 q^{79} - 10308 q^{80} - 4170 q^{82} + 10 q^{83} + 6830 q^{85} + 2 q^{86} + 990 q^{88} + 6820 q^{89} - 12 q^{91} + 1730 q^{92} + 3640 q^{94} - 3770 q^{95} + 9210 q^{97} + 3430 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(2475, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(825, [\chi])\)\(^{\oplus 2}\)