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Properties

Label 1575.4.dg
Level $1575$
Weight $4$
Character orbit 1575.dg
Rep. character $\chi_{1575}(206,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1920$
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.dg (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 525 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 5824 1920 3904
Cusp forms 5696 1920 3776
Eisenstein series 128 0 128

Trace form

\( 1920 q - 960 q^{4} - 24 q^{7} + O(q^{10}) \) \( 1920 q - 960 q^{4} - 24 q^{7} + 72 q^{10} + 3840 q^{16} - 1536 q^{22} - 180 q^{25} - 2160 q^{28} + 2484 q^{31} + 432 q^{37} + 3204 q^{40} - 672 q^{43} - 456 q^{46} + 1416 q^{49} - 1752 q^{58} + 26976 q^{64} - 2016 q^{67} - 9252 q^{70} + 7056 q^{73} + 168 q^{79} + 17352 q^{82} + 7968 q^{85} + 7128 q^{88} - 2088 q^{91} - 576 q^{94} + O(q^{100}) \)

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

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