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Properties

Label 2475.2.gf
Level $2475$
Weight $2$
Character orbit 2475.gf
Rep. character $\chi_{2475}(218,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $3392$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2475.gf (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 495 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2475, [\chi])\).

Total New Old
Modular forms 5952 3520 2432
Cusp forms 5568 3392 2176
Eisenstein series 384 128 256

Trace form

\( 3392 q + 18 q^{2} + 10 q^{3} - 24 q^{6} + 6 q^{7} + O(q^{10}) \) \( 3392 q + 18 q^{2} + 10 q^{3} - 24 q^{6} + 6 q^{7} - 24 q^{11} - 20 q^{12} + 6 q^{13} - 412 q^{16} + 20 q^{18} - 48 q^{21} + 48 q^{23} + 28 q^{27} + 8 q^{28} - 12 q^{31} + 62 q^{33} - 152 q^{36} + 36 q^{37} + 150 q^{38} - 36 q^{41} - 4 q^{42} + 16 q^{43} - 48 q^{46} + 42 q^{47} + 64 q^{48} - 184 q^{51} - 18 q^{52} + 240 q^{56} + 84 q^{57} + 58 q^{58} - 12 q^{61} + 4 q^{63} + 68 q^{66} - 8 q^{67} - 30 q^{68} + 14 q^{72} + 24 q^{73} - 64 q^{76} + 264 q^{77} + 104 q^{78} - 220 q^{81} + 8 q^{82} - 102 q^{83} + 72 q^{86} + 108 q^{87} - 92 q^{88} + 96 q^{91} - 234 q^{92} + 70 q^{93} - 320 q^{96} + 12 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2475, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2475, [\chi])\) into lower level spaces

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