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Properties

Label 1225.2.bi
Level $1225$
Weight $2$
Character orbit 1225.bi
Rep. character $\chi_{1225}(117,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $1536$
Sturm bound $280$

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Defining parameters

Level: \( N \) \(=\) \( 1225 = 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1225.bi (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(280\)

Dimensions

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

Total New Old
Modular forms 2368 1664 704
Cusp forms 2112 1536 576
Eisenstein series 256 128 128

Trace form

\( 1536 q + 8 q^{2} + 24 q^{3} + 10 q^{4} + 30 q^{5} - 60 q^{8} + 10 q^{9} + O(q^{10}) \) \( 1536 q + 8 q^{2} + 24 q^{3} + 10 q^{4} + 30 q^{5} - 60 q^{8} + 10 q^{9} + 36 q^{10} + 6 q^{11} + 36 q^{12} - 68 q^{15} - 162 q^{16} + 42 q^{17} + 46 q^{18} + 30 q^{19} - 192 q^{22} + 64 q^{23} - 10 q^{25} + 48 q^{26} - 160 q^{29} + 110 q^{30} + 18 q^{31} - 52 q^{32} + 30 q^{33} + 224 q^{36} + 18 q^{37} - 72 q^{38} - 70 q^{39} + 48 q^{40} + 4 q^{43} + 10 q^{44} - 186 q^{45} + 6 q^{46} + 54 q^{47} + 192 q^{50} + 16 q^{51} - 216 q^{52} + 106 q^{53} + 30 q^{54} + 152 q^{57} - 60 q^{58} - 90 q^{59} - 200 q^{60} + 18 q^{61} - 20 q^{64} - 30 q^{65} + 90 q^{66} - 12 q^{67} - 342 q^{68} - 48 q^{71} + 138 q^{72} + 6 q^{73} - 216 q^{75} - 140 q^{78} + 10 q^{79} + 6 q^{80} - 122 q^{81} - 216 q^{82} - 48 q^{85} + 6 q^{86} + 48 q^{87} + 266 q^{88} - 120 q^{89} - 108 q^{92} - 182 q^{93} + 30 q^{94} + 110 q^{95} + 90 q^{96} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1225, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)