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Properties

Label 1575.4.ck
Level $1575$
Weight $4$
Character orbit 1575.ck
Rep. character $\chi_{1575}(218,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1296$
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.ck (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
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 1296 1632
Cusp forms 2832 1296 1536
Eisenstein series 96 0 96

Trace form

\( 1296 q + 8 q^{3} + O(q^{10}) \) \( 1296 q + 8 q^{3} - 48 q^{11} - 128 q^{12} + 10368 q^{16} - 968 q^{18} + 224 q^{21} + 312 q^{23} + 1184 q^{27} - 1380 q^{32} - 1112 q^{33} + 1856 q^{36} + 288 q^{37} + 144 q^{38} + 3072 q^{41} + 280 q^{42} + 288 q^{46} + 6936 q^{47} + 7048 q^{48} + 1856 q^{51} - 1112 q^{57} - 1064 q^{63} + 17200 q^{66} + 1224 q^{67} - 872 q^{72} + 4464 q^{76} - 6936 q^{78} + 3968 q^{81} - 7488 q^{82} + 5640 q^{83} - 4176 q^{86} + 9568 q^{87} - 4176 q^{88} + 2016 q^{91} + 22668 q^{92} + 6872 q^{93} - 35904 q^{96} + 720 q^{97} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)