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Properties

Label 1575.4.cu
Level $1575$
Weight $4$
Character orbit 1575.cu
Rep. character $\chi_{1575}(433,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $2384$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1575.cu (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1575, [\chi])\).

Total New Old
Modular forms 5824 2416 3408
Cusp forms 5696 2384 3312
Eisenstein series 128 32 96

Trace form

\( 2384 q + 16 q^{2} - 20 q^{4} - 24 q^{7} - 36 q^{8} + O(q^{10}) \) \( 2384 q + 16 q^{2} - 20 q^{4} - 24 q^{7} - 36 q^{8} + 12 q^{11} + 10 q^{14} + 9332 q^{16} + 928 q^{22} - 328 q^{23} + 136 q^{25} - 778 q^{28} - 60 q^{29} - 892 q^{32} - 368 q^{35} - 568 q^{37} - 480 q^{43} + 20 q^{44} - 12 q^{46} - 5972 q^{50} + 2672 q^{53} + 262 q^{56} - 3112 q^{58} + 9640 q^{64} - 3040 q^{65} + 616 q^{67} + 1730 q^{70} + 12 q^{71} + 3778 q^{77} - 20 q^{79} - 5328 q^{85} + 12 q^{86} - 3420 q^{88} - 6 q^{91} + 4292 q^{92} - 9812 q^{95} - 13446 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1575, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1575, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)