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Properties

Label 2475.4.fs
Level $2475$
Weight $4$
Character orbit 2475.fs
Rep. character $\chi_{2475}(7,\cdot)$
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.fs (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

\( 10304 q + 10 q^{2} + 8 q^{3} - 40 q^{6} + 10 q^{7} + 40 q^{8} + O(q^{10}) \) \( 10304 q + 10 q^{2} + 8 q^{3} - 40 q^{6} + 10 q^{7} + 40 q^{8} - 32 q^{11} - 364 q^{12} + 10 q^{13} - 20236 q^{16} + 40 q^{17} + 20 q^{18} - 24 q^{22} + 944 q^{23} - 2224 q^{26} - 580 q^{27} + 40 q^{28} - 12 q^{31} - 1414 q^{33} - 312 q^{36} - 120 q^{37} + 46 q^{38} - 20 q^{41} + 1520 q^{42} - 80 q^{46} - 770 q^{47} + 984 q^{48} + 2040 q^{51} + 10 q^{52} - 1536 q^{53} - 4272 q^{56} + 580 q^{57} + 1582 q^{58} - 20 q^{61} - 15860 q^{62} + 20 q^{63} - 2800 q^{66} + 2464 q^{67} + 170 q^{68} + 11776 q^{71} - 3430 q^{72} + 40 q^{73} - 4564 q^{77} + 4296 q^{78} - 11544 q^{81} - 40 q^{82} + 10 q^{83} + 2076 q^{86} - 7592 q^{88} - 6096 q^{91} - 1790 q^{92} + 1852 q^{93} + 38400 q^{96} + 1158 q^{97} + O(q^{100}) \)

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

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