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Properties

Label 1575.2.cx
Level $1575$
Weight $2$
Character orbit 1575.cx
Rep. character $\chi_{1575}(8,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $480$
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.cx (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 75 \)
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 480 1504
Cusp forms 1856 480 1376
Eisenstein series 128 0 128

Trace form

\( 480 q + O(q^{10}) \) \( 480 q - 32 q^{10} + 8 q^{13} + 120 q^{16} + 80 q^{19} + 96 q^{22} + 16 q^{25} + 40 q^{34} - 8 q^{37} + 56 q^{40} - 80 q^{43} - 72 q^{52} + 32 q^{55} + 56 q^{58} - 320 q^{64} - 64 q^{67} - 16 q^{70} - 120 q^{73} - 160 q^{79} + 120 q^{82} - 40 q^{85} - 80 q^{88} + 160 q^{94} - 24 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)