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Properties

Label 1225.2.e
Level $1225$
Weight $2$
Character orbit 1225.e
Rep. character $\chi_{1225}(226,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $114$
Sturm bound $280$

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Defining parameters

Level: \( N \) \(=\) \( 1225 = 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1225.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(280\)

Dimensions

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

Total New Old
Modular forms 328 138 190
Cusp forms 232 114 118
Eisenstein series 96 24 72

Trace form

\( 114 q - 3 q^{2} - 2 q^{3} - 53 q^{4} + 16 q^{6} + 30 q^{8} - 43 q^{9} + O(q^{10}) \) \( 114 q - 3 q^{2} - 2 q^{3} - 53 q^{4} + 16 q^{6} + 30 q^{8} - 43 q^{9} + 6 q^{12} - 8 q^{13} - 53 q^{16} - 4 q^{17} - 5 q^{18} + 4 q^{19} + 8 q^{22} + 6 q^{23} - 12 q^{24} + 22 q^{26} + 4 q^{27} + 20 q^{29} + 2 q^{31} - 3 q^{32} - 12 q^{33} + 16 q^{34} - 54 q^{36} + 14 q^{37} - 8 q^{38} + 52 q^{39} + 4 q^{41} + 12 q^{43} - 34 q^{44} - 54 q^{46} - 4 q^{47} + 12 q^{48} - 2 q^{51} + 20 q^{52} - 18 q^{53} - 38 q^{54} - 56 q^{57} - 16 q^{58} + 2 q^{59} + 18 q^{61} - 24 q^{62} + 114 q^{64} + 48 q^{66} - 18 q^{67} - 20 q^{68} - 48 q^{69} - 60 q^{71} - 41 q^{72} - 4 q^{73} - 54 q^{74} - 68 q^{76} + 112 q^{78} + 22 q^{79} - 13 q^{81} + 18 q^{82} + 4 q^{83} - 6 q^{86} + 2 q^{87} + 32 q^{88} - 60 q^{92} + 16 q^{93} - 30 q^{94} + 14 q^{96} + 24 q^{97} - 84 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1225, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 3}\)