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Properties

Label 1575.2.cf
Level $1575$
Weight $2$
Character orbit 1575.cf
Rep. character $\chi_{1575}(32,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $560$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1575.cf (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1575, [\chi])\).

Total New Old
Modular forms 1008 592 416
Cusp forms 912 560 352
Eisenstein series 96 32 64

Trace form

\( 560 q + 6 q^{2} + 2 q^{3} + 2 q^{7} + O(q^{10}) \) \( 560 q + 6 q^{2} + 2 q^{3} + 2 q^{7} + 22 q^{12} + 4 q^{13} + 260 q^{16} + 18 q^{17} + 10 q^{18} - 64 q^{21} - 4 q^{22} + 32 q^{27} + 4 q^{28} + 4 q^{31} + 90 q^{32} - 32 q^{33} - 16 q^{36} + 4 q^{37} - 14 q^{42} + 4 q^{43} - 32 q^{46} + 6 q^{47} - 38 q^{48} - 52 q^{51} + 52 q^{52} + 156 q^{56} - 32 q^{57} + 12 q^{58} + 28 q^{61} - 14 q^{63} + 244 q^{66} - 2 q^{67} + 46 q^{72} + 4 q^{73} - 24 q^{76} - 42 q^{77} - 54 q^{78} - 52 q^{81} + 8 q^{82} + 12 q^{83} + 28 q^{87} - 12 q^{88} - 16 q^{91} - 72 q^{92} - 4 q^{93} + 36 q^{96} + 4 q^{97} - 12 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1575, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1575, [\chi])\) into lower level spaces

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