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Properties

Label 1225.2.bd
Level $1225$
Weight $2$
Character orbit 1225.bd
Rep. character $\chi_{1225}(36,\cdot)$
Character field $\Q(\zeta_{35})$
Dimension $3312$
Sturm bound $280$

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Defining parameters

Level: \( N \) \(=\) \( 1225 = 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1225.bd (of order \(35\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1225 \)
Character field: \(\Q(\zeta_{35})\)
Sturm bound: \(280\)

Dimensions

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

Total New Old
Modular forms 3408 3408 0
Cusp forms 3312 3312 0
Eisenstein series 96 96 0

Trace form

\( 3312 q - 15 q^{2} - 15 q^{3} + 121 q^{4} - 22 q^{5} - 27 q^{6} - 54 q^{7} - 5 q^{8} + 119 q^{9} + O(q^{10}) \) \( 3312 q - 15 q^{2} - 15 q^{3} + 121 q^{4} - 22 q^{5} - 27 q^{6} - 54 q^{7} - 5 q^{8} + 119 q^{9} - 34 q^{10} - 30 q^{11} - 35 q^{12} - 15 q^{13} - 18 q^{14} - 22 q^{15} + 109 q^{16} - 42 q^{17} - 116 q^{18} + 12 q^{19} - 18 q^{20} - 15 q^{21} - 3 q^{22} + 9 q^{23} - 28 q^{24} - 34 q^{25} - 33 q^{27} - 22 q^{28} - 15 q^{29} - 16 q^{30} + 48 q^{31} - 4 q^{32} - 21 q^{33} + 49 q^{34} - 31 q^{35} + 55 q^{36} - 27 q^{37} + 7 q^{38} - 47 q^{39} - 4 q^{40} - 13 q^{41} + 60 q^{42} + 4 q^{43} - 55 q^{44} - 152 q^{45} - 63 q^{46} - 13 q^{47} - 108 q^{48} - 70 q^{49} - 514 q^{50} - 76 q^{51} + 95 q^{52} + 35 q^{53} - 108 q^{54} + 38 q^{55} - 9 q^{56} + 148 q^{57} + 25 q^{58} - 15 q^{59} - 210 q^{60} - 31 q^{61} + 41 q^{62} - 27 q^{63} + 123 q^{64} - 62 q^{65} - 107 q^{66} - 32 q^{67} + 12 q^{68} - q^{69} + 72 q^{70} - 60 q^{71} - 346 q^{72} - 11 q^{73} - 92 q^{74} + 158 q^{75} + 222 q^{76} - 29 q^{77} - 25 q^{78} - 68 q^{79} + 30 q^{80} + 63 q^{81} + 120 q^{82} - 56 q^{83} - 257 q^{84} + 18 q^{85} + 57 q^{86} - 75 q^{87} - 200 q^{88} - 114 q^{89} + 20 q^{90} - q^{91} - 25 q^{92} + 180 q^{93} - 71 q^{94} - 9 q^{95} + 23 q^{96} + 168 q^{97} - 296 q^{98} - 164 q^{99} + O(q^{100}) \)

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.