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Properties

Label 1225.2.f
Level $1225$
Weight $2$
Character orbit 1225.f
Rep. character $\chi_{1225}(293,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $112$
Sturm bound $280$

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Defining parameters

Level: \( N \) \(=\) \( 1225 = 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1225.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(i)\)
Sturm bound: \(280\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1225, [\chi])\).

Total New Old
Modular forms 328 128 200
Cusp forms 232 112 120
Eisenstein series 96 16 80

Trace form

\( 112 q - 4 q^{2} + 4 q^{8} + O(q^{10}) \) \( 112 q - 4 q^{2} + 4 q^{8} + 8 q^{11} - 48 q^{16} - 24 q^{18} + 24 q^{22} + 4 q^{23} + 44 q^{32} - 232 q^{36} - 32 q^{37} - 4 q^{43} + 64 q^{46} + 88 q^{51} + 48 q^{53} + 48 q^{57} + 76 q^{58} + 4 q^{67} - 32 q^{71} - 32 q^{72} - 96 q^{78} - 8 q^{81} + 160 q^{86} - 16 q^{88} + 4 q^{92} - 24 q^{93} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1225, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1225, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1225, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)