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Properties

Label 1575.4.ba
Level $1575$
Weight $4$
Character orbit 1575.ba
Rep. character $\chi_{1575}(524,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $856$
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.ba (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 1464 872 592
Cusp forms 1416 856 560
Eisenstein series 48 16 32

Trace form

\( 856 q - 1692 q^{4} + 16 q^{9} + O(q^{10}) \) \( 856 q - 1692 q^{4} + 16 q^{9} + 12 q^{11} + 270 q^{14} - 6628 q^{16} - 138 q^{21} + 516 q^{29} + 828 q^{36} + 1572 q^{39} - 2096 q^{46} - 394 q^{49} + 1632 q^{51} + 2784 q^{56} + 50768 q^{64} + 108 q^{74} - 428 q^{79} + 8672 q^{81} - 2214 q^{84} + 8280 q^{86} - 1380 q^{91} + 2444 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)