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Properties

Label 3525.2.x
Level $3525$
Weight $2$
Character orbit 3525.x
Rep. character $\chi_{3525}(187,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1920$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3525.x (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1175 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3525, [\chi])\).

Total New Old
Modular forms 3872 1920 1952
Cusp forms 3808 1920 1888
Eisenstein series 64 0 64

Trace form

\( 1920 q - 8 q^{7} - 24 q^{8} + O(q^{10}) \) \( 1920 q - 8 q^{7} - 24 q^{8} - 16 q^{12} + 480 q^{16} + 32 q^{17} - 8 q^{25} + 56 q^{28} - 48 q^{32} - 480 q^{36} + 24 q^{37} - 72 q^{47} + 32 q^{48} + 320 q^{50} + 8 q^{53} + 168 q^{55} - 8 q^{63} + 40 q^{64} - 24 q^{65} - 24 q^{68} + 24 q^{72} - 48 q^{75} + 480 q^{81} - 152 q^{83} + 40 q^{94} - 264 q^{95} + 40 q^{96} - 40 q^{97} + 440 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3525, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3525, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3525, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1175, [\chi])\)\(^{\oplus 2}\)