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Properties

Label 225.10.s
Level $225$
Weight $10$
Character orbit 225.s
Rep. character $\chi_{225}(8,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $720$
Sturm bound $300$

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Defining parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 225.s (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 75 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(300\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(225, [\chi])\).

Total New Old
Modular forms 2192 720 1472
Cusp forms 2128 720 1408
Eisenstein series 64 0 64

Trace form

\( 720 q - 19512 q^{7} + O(q^{10}) \) \( 720 q - 19512 q^{7} - 79632 q^{10} + 2916 q^{13} + 11796480 q^{16} - 4497840 q^{19} + 7420752 q^{22} + 5770224 q^{25} + 46926432 q^{28} + 51353280 q^{34} - 37268964 q^{37} + 191944152 q^{40} - 173814048 q^{43} - 143038584 q^{52} + 380977992 q^{55} - 173382192 q^{58} + 3365314560 q^{64} - 577869696 q^{67} - 2869633584 q^{70} + 2247904836 q^{73} - 2724023520 q^{79} - 652113936 q^{82} + 2739006972 q^{85} - 7467913296 q^{88} + 4529938320 q^{94} - 7733557476 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(225, [\chi])\) into newform subspaces

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

Decomposition of \(S_{10}^{\mathrm{old}}(225, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(225, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)