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Properties

Label 1575.2.cu
Level $1575$
Weight $2$
Character orbit 1575.cu
Rep. character $\chi_{1575}(433,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $784$
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.cu (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1984 816 1168
Cusp forms 1856 784 1072
Eisenstein series 128 32 96

Trace form

\( 784 q + 16 q^{2} - 20 q^{4} - 6 q^{7} + 36 q^{8} + O(q^{10}) \) \( 784 q + 16 q^{2} - 20 q^{4} - 6 q^{7} + 36 q^{8} + 12 q^{11} + 10 q^{14} + 172 q^{16} - 32 q^{22} + 8 q^{23} - 4 q^{25} + 58 q^{28} + 40 q^{29} + 68 q^{32} + 12 q^{35} - 12 q^{37} + 56 q^{43} + 20 q^{44} - 12 q^{46} + 148 q^{50} - 32 q^{53} + 22 q^{56} - 32 q^{58} + 40 q^{64} + 60 q^{65} - 80 q^{67} - 110 q^{70} + 12 q^{71} - 98 q^{77} - 20 q^{79} + 32 q^{85} + 12 q^{86} - 196 q^{88} - 6 q^{91} - 20 q^{92} + 8 q^{95} + 22 q^{98} + O(q^{100}) \)

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

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