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Properties

Label 1225.2.t
Level $1225$
Weight $2$
Character orbit 1225.t
Rep. character $\chi_{1225}(274,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $492$
Sturm bound $280$

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Defining parameters

Level: \( N \) \(=\) \( 1225 = 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1225.t (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(280\)

Dimensions

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

Total New Old
Modular forms 876 516 360
Cusp forms 804 492 312
Eisenstein series 72 24 48

Trace form

\( 492 q + 90 q^{4} + 22 q^{6} + 68 q^{9} + O(q^{10}) \) \( 492 q + 90 q^{4} + 22 q^{6} + 68 q^{9} - 28 q^{11} + 18 q^{14} - 94 q^{16} + 76 q^{19} - 14 q^{21} - 14 q^{24} + 14 q^{26} - 42 q^{29} - 92 q^{31} + 34 q^{34} - 14 q^{36} - 12 q^{39} + 6 q^{41} - 130 q^{44} + 90 q^{46} - 32 q^{49} + 66 q^{51} - 4 q^{54} + 52 q^{56} - 38 q^{59} - 44 q^{61} + 10 q^{64} + 174 q^{66} + 2 q^{69} + 32 q^{71} - 6 q^{74} - 228 q^{76} - 8 q^{79} + 84 q^{81} + 178 q^{84} - 158 q^{86} + 132 q^{89} + 130 q^{91} - 74 q^{94} + 190 q^{96} - 196 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1225, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 2}\)