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Properties

Label 1225.4.b
Level $1225$
Weight $4$
Character orbit 1225.b
Rep. character $\chi_{1225}(99,\cdot)$
Character field $\Q$
Dimension $180$
Sturm bound $560$

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Defining parameters

Level: \( N \) \(=\) \( 1225 = 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1225.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Sturm bound: \(560\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1225, [\chi])\).

Total New Old
Modular forms 444 190 254
Cusp forms 396 180 216
Eisenstein series 48 10 38

Trace form

\( 180 q - 694 q^{4} + 26 q^{6} - 1522 q^{9} + O(q^{10}) \) \( 180 q - 694 q^{4} + 26 q^{6} - 1522 q^{9} + 110 q^{11} + 2726 q^{16} + 226 q^{19} - 94 q^{24} - 700 q^{26} + 180 q^{29} + 300 q^{31} + 1302 q^{34} + 5240 q^{36} - 512 q^{39} - 1206 q^{41} - 714 q^{44} + 692 q^{46} + 1654 q^{51} - 3138 q^{54} + 532 q^{59} - 1592 q^{61} - 12578 q^{64} + 3614 q^{66} + 5004 q^{69} + 928 q^{71} + 5952 q^{74} - 3686 q^{76} - 4944 q^{79} + 12924 q^{81} + 4320 q^{86} - 206 q^{89} - 2604 q^{94} + 10150 q^{96} + 1228 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1225, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1225, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1225, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 3}\)