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Properties

Label 1225.2.bu
Level $1225$
Weight $2$
Character orbit 1225.bu
Rep. character $\chi_{1225}(3,\cdot)$
Character field $\Q(\zeta_{420})$
Dimension $13248$
Sturm bound $280$

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Defining parameters

Level: \( N \) \(=\) \( 1225 = 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1225.bu (of order \(420\) and degree \(96\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1225 \)
Character field: \(\Q(\zeta_{420})\)
Sturm bound: \(280\)

Dimensions

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

Total New Old
Modular forms 13632 13632 0
Cusp forms 13248 13248 0
Eisenstein series 384 384 0

Trace form

\( 13248 q - 104 q^{2} - 88 q^{3} - 130 q^{4} - 82 q^{5} - 84 q^{6} - 102 q^{7} - 76 q^{8} - 130 q^{9} + O(q^{10}) \) \( 13248 q - 104 q^{2} - 88 q^{3} - 130 q^{4} - 82 q^{5} - 84 q^{6} - 102 q^{7} - 76 q^{8} - 130 q^{9} - 76 q^{10} - 78 q^{11} - 76 q^{12} - 112 q^{13} - 120 q^{14} - 112 q^{15} + 186 q^{16} - 14 q^{17} - 50 q^{18} - 180 q^{19} - 112 q^{20} - 72 q^{21} - 52 q^{22} - 96 q^{23} - 106 q^{25} - 176 q^{26} - 112 q^{27} - 134 q^{28} - 100 q^{29} - 50 q^{30} - 108 q^{31} - 184 q^{32} - 82 q^{33} - 140 q^{34} - 110 q^{35} - 604 q^{36} - 110 q^{37} - 212 q^{38} - 130 q^{39} - 64 q^{40} - 84 q^{41} - 6 q^{42} + 4 q^{43} - 130 q^{44} + 150 q^{45} - 78 q^{46} - 16 q^{47} - 1024 q^{50} - 208 q^{51} - 328 q^{52} - 24 q^{53} - 110 q^{54} - 154 q^{55} - 88 q^{56} - 12 q^{57} + 12 q^{58} - 230 q^{59} - 104 q^{60} - 66 q^{61} - 84 q^{62} - 46 q^{63} - 40 q^{64} - 110 q^{65} + 6 q^{66} - 52 q^{67} - 510 q^{68} - 140 q^{69} - 220 q^{70} - 60 q^{71} - 328 q^{72} - 106 q^{73} - 244 q^{75} - 336 q^{76} - 32 q^{77} + 164 q^{78} - 60 q^{79} - 162 q^{80} + 166 q^{81} - 188 q^{82} + 168 q^{83} - 1000 q^{84} - 64 q^{85} - 78 q^{86} - 36 q^{87} - 418 q^{88} + 90 q^{89} - 448 q^{90} - 72 q^{91} - 92 q^{92} - 498 q^{93} - 110 q^{94} - 156 q^{95} + 6 q^{96} + 1276 q^{98} + O(q^{100}) \)

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.