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Properties

Label 1225.2.u
Level $1225$
Weight $2$
Character orbit 1225.u
Rep. character $\chi_{1225}(116,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $768$
Sturm bound $280$

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Defining parameters

Level: \( N \) \(=\) \( 1225 = 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1225.u (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(280\)

Dimensions

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

Total New Old
Modular forms 1184 832 352
Cusp forms 1056 768 288
Eisenstein series 128 64 64

Trace form

\( 768 q + 3 q^{2} + 3 q^{3} + 95 q^{4} + 3 q^{5} + 12 q^{6} - 34 q^{8} + 91 q^{9} + O(q^{10}) \) \( 768 q + 3 q^{2} + 3 q^{3} + 95 q^{4} + 3 q^{5} + 12 q^{6} - 34 q^{8} + 91 q^{9} + 3 q^{10} + 6 q^{11} + 11 q^{12} + 12 q^{13} + 48 q^{15} + 83 q^{16} - 9 q^{17} + 2 q^{18} + 11 q^{19} + 24 q^{20} + 40 q^{22} + 19 q^{23} - 46 q^{24} + 9 q^{25} - 44 q^{26} + 84 q^{27} + 7 q^{30} + 21 q^{31} + 12 q^{32} + 18 q^{33} + 36 q^{34} - 40 q^{36} + 13 q^{37} + 12 q^{38} - 37 q^{39} - q^{40} - 38 q^{41} - 124 q^{43} - 41 q^{44} + 45 q^{45} - 57 q^{46} + q^{47} + 12 q^{48} - 102 q^{50} - 28 q^{51} - 50 q^{52} + 17 q^{53} - 15 q^{54} + 28 q^{55} - 296 q^{57} - 129 q^{58} + 39 q^{59} - 67 q^{60} + 13 q^{61} - 124 q^{62} - 270 q^{64} + 7 q^{65} - 7 q^{66} + 21 q^{67} + 110 q^{68} - 50 q^{69} - 74 q^{71} + 188 q^{72} + 41 q^{73} - 54 q^{74} - 27 q^{75} + 276 q^{76} + 42 q^{78} - 5 q^{79} + 94 q^{80} - 27 q^{81} + 108 q^{82} - 86 q^{83} - 190 q^{85} + 37 q^{86} + 7 q^{87} - 10 q^{88} + 42 q^{89} - 376 q^{90} + 66 q^{92} - 214 q^{93} + 11 q^{94} - 99 q^{95} - 13 q^{96} - 96 q^{97} - 60 q^{99} + O(q^{100}) \)

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

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