Properties

Label 1575.2.ch
Level $1575$
Weight $2$
Character orbit 1575.ch
Rep. character $\chi_{1575}(82,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $232$
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.ch (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
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 1056 248 808
Cusp forms 864 232 632
Eisenstein series 192 16 176

Trace form

\( 232 q - 2 q^{2} + 2 q^{7} - 28 q^{8} + O(q^{10}) \) \( 232 q - 2 q^{2} + 2 q^{7} - 28 q^{8} + 4 q^{11} + 84 q^{16} + 12 q^{17} + 8 q^{22} + 2 q^{23} + 36 q^{26} + 70 q^{28} + 12 q^{31} + 6 q^{32} + 16 q^{37} + 28 q^{43} - 8 q^{46} - 36 q^{47} - 24 q^{52} - 4 q^{53} + 8 q^{56} - 66 q^{58} + 48 q^{61} - 18 q^{67} + 120 q^{68} + 64 q^{71} - 48 q^{73} + 40 q^{77} - 18 q^{82} + 112 q^{86} - 16 q^{88} - 52 q^{91} - 92 q^{92} - 54 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)