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Properties

Label 2475.4.dr
Level $2475$
Weight $4$
Character orbit 2475.dr
Rep. character $\chi_{2475}(208,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $3584$
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.dr (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 8704 3616 5088
Cusp forms 8576 3584 4992
Eisenstein series 128 32 96

Trace form

\( 3584 q - 20 q^{4} + O(q^{10}) \) \( 3584 q - 20 q^{4} + 6 q^{11} + 20 q^{14} + 14132 q^{16} + 524 q^{20} - 778 q^{22} + 244 q^{23} - 512 q^{25} + 32 q^{26} - 12 q^{31} - 20 q^{34} - 184 q^{37} + 972 q^{38} - 1320 q^{44} - 3000 q^{47} - 1508 q^{53} - 150 q^{55} + 524 q^{56} + 3288 q^{58} + 1680 q^{59} - 5780 q^{64} - 284 q^{67} - 6660 q^{70} + 1252 q^{71} - 4242 q^{77} + 3852 q^{80} - 13980 q^{82} + 12 q^{86} + 9710 q^{88} - 13580 q^{89} - 12 q^{91} + 800 q^{92} - 19720 q^{97} + O(q^{100}) \)

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

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