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Properties

Label 1225.2.bj
Level $1225$
Weight $2$
Character orbit 1225.bj
Rep. character $\chi_{1225}(29,\cdot)$
Character field $\Q(\zeta_{70})$
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.bj (of order \(70\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1225 \)
Character field: \(\Q(\zeta_{70})\)
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

\( 3312 q - 25 q^{2} - 25 q^{3} - 151 q^{4} - 22 q^{5} - 3 q^{6} - 55 q^{8} - 149 q^{9} + O(q^{10}) \) \( 3312 q - 25 q^{2} - 25 q^{3} - 151 q^{4} - 22 q^{5} - 3 q^{6} - 55 q^{8} - 149 q^{9} - 14 q^{10} - 25 q^{12} - 25 q^{13} - 30 q^{14} - 10 q^{15} + 125 q^{16} - 50 q^{17} + 12 q^{19} - 38 q^{20} - 21 q^{21} - 25 q^{22} - 65 q^{23} + 12 q^{24} - 10 q^{25} - 80 q^{26} - 55 q^{27} - 20 q^{28} - 15 q^{29} - 124 q^{30} - 120 q^{31} - 75 q^{33} + 65 q^{34} - 45 q^{35} + 139 q^{36} - 25 q^{37} + 5 q^{38} - 23 q^{39} - 116 q^{40} - 17 q^{41} - 70 q^{42} - 39 q^{44} - 240 q^{45} + 33 q^{46} - 25 q^{47} - 40 q^{48} - 70 q^{49} - 478 q^{50} - 4 q^{51} - 15 q^{52} - 25 q^{53} - 2 q^{54} - 76 q^{55} - 43 q^{56} - 25 q^{58} - 15 q^{59} + 90 q^{60} + q^{61} - 25 q^{62} - 65 q^{63} - 149 q^{64} - 14 q^{65} + 29 q^{66} - 120 q^{67} + 23 q^{69} + 18 q^{70} + 30 q^{71} + 480 q^{72} - 105 q^{73} - 76 q^{74} - 42 q^{75} - 222 q^{76} - 25 q^{77} + 5 q^{78} - 68 q^{79} - 262 q^{80} + 151 q^{81} - 160 q^{83} - 279 q^{84} - 122 q^{85} - 87 q^{86} - 25 q^{87} + 190 q^{88} - 114 q^{89} - 152 q^{90} - 35 q^{91} - 115 q^{92} - 55 q^{94} - 41 q^{95} - 53 q^{96} + 80 q^{97} - 480 q^{98} - 140 q^{99} + O(q^{100}) \)

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.