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Properties

Label 2475.4.cf
Level $2475$
Weight $4$
Character orbit 2475.cf
Rep. character $\chi_{2475}(874,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $1072$
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.cf (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
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 4416 1088 3328
Cusp forms 4224 1072 3152
Eisenstein series 192 16 176

Trace form

\( 1072 q + 1070 q^{4} + O(q^{10}) \) \( 1072 q + 1070 q^{4} + 56 q^{11} - 102 q^{14} - 3894 q^{16} + 342 q^{19} - 1028 q^{26} - 770 q^{29} + 354 q^{31} - 1232 q^{34} - 862 q^{41} + 362 q^{44} - 1836 q^{46} + 14866 q^{49} - 4264 q^{56} + 536 q^{59} - 858 q^{61} + 8202 q^{64} + 4642 q^{71} + 3398 q^{74} + 5636 q^{76} + 1514 q^{79} + 58 q^{86} + 4424 q^{89} + 1190 q^{91} + 5308 q^{94} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(2475, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 2}\)