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Properties

Label 2475.4.co
Level $2475$
Weight $4$
Character orbit 2475.co
Rep. character $\chi_{2475}(161,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $1440$
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.co (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 825 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 4352 1440 2912
Cusp forms 4288 1440 2848
Eisenstein series 64 0 64

Trace form

\( 1440 q + 5760 q^{4} - 60 q^{7} + O(q^{10}) \) \( 1440 q + 5760 q^{4} - 60 q^{7} - 120 q^{10} - 480 q^{13} + 22608 q^{16} - 1224 q^{22} - 612 q^{25} - 720 q^{28} - 276 q^{31} + 216 q^{37} - 1440 q^{40} - 2160 q^{46} + 18348 q^{49} - 7680 q^{52} + 708 q^{55} + 2064 q^{58} + 1440 q^{61} + 86832 q^{64} + 2208 q^{67} - 4848 q^{70} + 420 q^{79} + 10512 q^{82} + 1680 q^{85} - 14352 q^{88} + 288 q^{91} - 2760 q^{94} + 300 q^{97} + O(q^{100}) \)

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

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