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Properties

Label 1575.4.cd
Level $1575$
Weight $4$
Character orbit 1575.cd
Rep. character $\chi_{1575}(893,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1712$
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.cd (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 2928 1744 1184
Cusp forms 2832 1712 1120
Eisenstein series 96 32 64

Trace form

\( 1712 q + 2 q^{3} - 48 q^{6} + 2 q^{7} + O(q^{10}) \) \( 1712 q + 2 q^{3} - 48 q^{6} + 2 q^{7} - 60 q^{11} - 230 q^{12} + 4 q^{13} - 26632 q^{16} + 144 q^{17} + 82 q^{18} - 760 q^{21} - 28 q^{22} + 318 q^{23} - 4 q^{27} - 104 q^{28} - 8 q^{31} - 530 q^{33} - 2128 q^{36} + 4 q^{37} + 102 q^{38} + 2448 q^{41} + 520 q^{42} + 4 q^{43} + 1000 q^{46} - 1778 q^{48} + 1772 q^{51} - 290 q^{52} - 6348 q^{56} - 68 q^{57} + 534 q^{58} - 152 q^{61} - 2468 q^{63} + 172 q^{66} + 4 q^{67} + 1542 q^{68} + 4186 q^{72} + 4 q^{73} - 264 q^{76} - 3258 q^{77} - 654 q^{78} - 6964 q^{81} + 20 q^{82} + 12 q^{83} - 16644 q^{86} - 110 q^{87} + 798 q^{88} - 16 q^{91} - 3780 q^{92} - 3886 q^{93} + 6420 q^{96} + 4 q^{97} + 48 q^{98} + O(q^{100}) \)

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

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