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Properties

Label 1575.2.dg
Level $1575$
Weight $2$
Character orbit 1575.dg
Rep. character $\chi_{1575}(206,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $640$
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.dg (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 525 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1984 640 1344
Cusp forms 1856 640 1216
Eisenstein series 128 0 128

Trace form

\( 640 q - 80 q^{4} + 8 q^{7} + O(q^{10}) \) \( 640 q - 80 q^{4} + 8 q^{7} + 12 q^{10} + 80 q^{16} + 32 q^{22} + 4 q^{25} + 100 q^{28} + 36 q^{31} + 16 q^{37} - 24 q^{40} + 16 q^{43} - 64 q^{46} + 16 q^{49} + 96 q^{58} + 256 q^{64} + 32 q^{67} + 120 q^{70} - 168 q^{73} + 8 q^{79} - 264 q^{82} - 8 q^{85} - 84 q^{88} + 68 q^{91} - 96 q^{94} + O(q^{100}) \)

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

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