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Properties

Label 2475.4.gf
Level $2475$
Weight $4$
Character orbit 2475.gf
Rep. character $\chi_{2475}(218,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $10304$
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.gf (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 495 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 17472 10432 7040
Cusp forms 17088 10304 6784
Eisenstein series 384 128 256

Trace form

\( 10304 q + 18 q^{2} + 16 q^{3} - 24 q^{6} + 6 q^{7} + O(q^{10}) \) \( 10304 q + 18 q^{2} + 16 q^{3} - 24 q^{6} + 6 q^{7} - 96 q^{11} + 148 q^{12} + 6 q^{13} - 20236 q^{16} + 44 q^{18} + 384 q^{21} - 24 q^{22} + 48 q^{23} + 604 q^{27} - 424 q^{28} - 12 q^{31} - 720 q^{32} - 1522 q^{33} + 1288 q^{36} + 168 q^{37} - 102 q^{38} - 36 q^{41} + 3464 q^{42} + 16 q^{43} - 48 q^{46} + 2346 q^{47} + 3544 q^{48} - 904 q^{51} - 474 q^{52} - 15888 q^{56} + 564 q^{57} - 1442 q^{58} - 12 q^{61} - 200 q^{63} + 8480 q^{66} - 2432 q^{67} - 750 q^{68} - 6442 q^{72} + 24 q^{73} - 544 q^{76} + 9624 q^{77} - 4168 q^{78} - 7192 q^{81} - 40 q^{82} + 5658 q^{83} + 6228 q^{86} - 2292 q^{87} + 9112 q^{88} - 6096 q^{91} + 18846 q^{92} + 13588 q^{93} + 34000 q^{96} + 1158 q^{97} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(2475, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 2}\)