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Properties

Label 1225.2.be
Level $1225$
Weight $2$
Character orbit 1225.be
Rep. character $\chi_{1225}(74,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $984$
Sturm bound $280$

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Defining parameters

Level: \( N \) \(=\) \( 1225 = 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1225.be (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(280\)

Dimensions

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

Total New Old
Modular forms 1752 1032 720
Cusp forms 1608 984 624
Eisenstein series 144 48 96

Trace form

\( 984 q - 54 q^{4} - 40 q^{6} - 20 q^{9} + O(q^{10}) \) \( 984 q - 54 q^{4} - 40 q^{6} - 20 q^{9} - 14 q^{11} + 54 q^{14} + 46 q^{16} - 34 q^{19} - 34 q^{21} + 44 q^{24} - 50 q^{26} + 72 q^{29} + 56 q^{31} - 28 q^{34} - 232 q^{36} + 36 q^{39} + 72 q^{41} - 62 q^{44} + 138 q^{46} - 40 q^{49} + 78 q^{51} - 140 q^{54} + 146 q^{56} + 26 q^{59} - 58 q^{61} + 224 q^{64} - 180 q^{66} + 52 q^{69} - 62 q^{71} + 72 q^{74} + 114 q^{76} - 4 q^{79} - 174 q^{81} - 142 q^{84} + 26 q^{86} - 18 q^{89} - 106 q^{91} + 194 q^{94} - 322 q^{96} + 268 q^{99} + O(q^{100}) \)

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

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