Properties

Label 2475.4.s
Level $2475$
Weight $4$
Character orbit 2475.s
Rep. character $\chi_{2475}(91,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $1792$
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.s (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 4352 1808 2544
Cusp forms 4288 1792 2496
Eisenstein series 64 16 48

Trace form

\( 1792 q + 6 q^{2} + 7130 q^{4} - 9 q^{5} - 14 q^{7} + 54 q^{8} + O(q^{10}) \) \( 1792 q + 6 q^{2} + 7130 q^{4} - 9 q^{5} - 14 q^{7} + 54 q^{8} + 76 q^{10} + 31 q^{11} - 145 q^{13} + 9 q^{14} + 28450 q^{16} - 31 q^{17} + 554 q^{19} - 163 q^{20} - 17 q^{22} - 222 q^{23} - 125 q^{25} + 59 q^{26} - 537 q^{28} - 1386 q^{29} + 101 q^{31} - 62 q^{32} - 14 q^{34} + 723 q^{35} + 263 q^{37} - 934 q^{38} - 298 q^{40} + 465 q^{41} + 56 q^{43} + 401 q^{44} - 201 q^{46} - 1341 q^{47} - 21040 q^{49} + 150 q^{50} - 4249 q^{52} - 1693 q^{53} + 1097 q^{55} + 421 q^{56} + 1286 q^{58} - 739 q^{59} - 1041 q^{61} + 3074 q^{62} + 113330 q^{64} + 1185 q^{65} + 1380 q^{67} + 1787 q^{68} + 4023 q^{70} + 1269 q^{71} - 2785 q^{73} + 2033 q^{74} + 394 q^{76} - 2591 q^{77} - 1665 q^{79} - 2276 q^{80} + 7184 q^{82} + 2175 q^{83} + 985 q^{85} - 830 q^{86} - 1637 q^{88} - 2634 q^{89} + 825 q^{91} - 14170 q^{92} + 2707 q^{94} + 7084 q^{95} - 5875 q^{97} - 5122 q^{98} + O(q^{100}) \)

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

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