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Properties

Label 1575.4.cj
Level $1575$
Weight $4$
Character orbit 1575.cj
Rep. character $\chi_{1575}(643,\cdot)$
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.cj (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

\( 1712 q + 4 q^{2} + 2 q^{7} + 80 q^{8} + O(q^{10}) \) \( 1712 q + 4 q^{2} + 2 q^{7} + 80 q^{8} - 24 q^{11} + 13304 q^{16} + 56 q^{18} + 744 q^{21} - 60 q^{22} + 108 q^{23} + 296 q^{28} + 144 q^{32} + 3184 q^{36} + 16 q^{37} + 1318 q^{42} + 4 q^{43} - 4064 q^{46} - 544 q^{51} - 2224 q^{53} - 5260 q^{56} + 1864 q^{57} - 940 q^{58} + 4134 q^{63} + 4 q^{67} + 4640 q^{71} - 2308 q^{72} + 790 q^{77} + 3692 q^{78} - 11968 q^{81} + 3464 q^{86} + 2532 q^{88} - 16 q^{91} + 1796 q^{92} + 5252 q^{93} + 432 q^{98} + O(q^{100}) \)

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

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