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Properties

Label 1225.2.k
Level $1225$
Weight $2$
Character orbit 1225.k
Rep. character $\chi_{1225}(324,\cdot)$
Character field $\Q(\zeta_{6})$
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.k (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
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

\( 112 q + 50 q^{4} + 16 q^{6} + 42 q^{9} + O(q^{10}) \) \( 112 q + 50 q^{4} + 16 q^{6} + 42 q^{9} + 8 q^{11} - 46 q^{16} + 8 q^{19} + 16 q^{24} + 6 q^{26} - 16 q^{29} - 14 q^{31} + 60 q^{36} - 44 q^{39} + 44 q^{41} - 46 q^{44} - 6 q^{46} + 70 q^{51} + 42 q^{54} + 26 q^{59} - 2 q^{61} - 204 q^{64} + 44 q^{66} + 24 q^{69} - 52 q^{71} - 36 q^{74} - 124 q^{76} - 50 q^{79} - 56 q^{81} - 66 q^{86} + 24 q^{89} + 26 q^{94} + 14 q^{96} + 76 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1225, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 2}\)