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Properties

Label 3025.2.k
Level $3025$
Weight $2$
Character orbit 3025.k
Rep. character $\chi_{3025}(1291,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $1048$
Sturm bound $660$

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Defining parameters

Level: \( N \) \(=\) \( 3025 = 5^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3025.k (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(660\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3025, [\chi])\).

Total New Old
Modular forms 1368 1112 256
Cusp forms 1272 1048 224
Eisenstein series 96 64 32

Trace form

\( 1048 q + q^{2} + 2 q^{3} - 253 q^{4} + 4 q^{5} - q^{6} + 9 q^{7} - 7 q^{8} + 986 q^{9} + O(q^{10}) \) \( 1048 q + q^{2} + 2 q^{3} - 253 q^{4} + 4 q^{5} - q^{6} + 9 q^{7} - 7 q^{8} + 986 q^{9} + 12 q^{10} + 24 q^{12} - 2 q^{13} - 7 q^{14} + 14 q^{15} - 241 q^{16} + 2 q^{17} + 21 q^{18} - 5 q^{19} - 15 q^{20} + q^{21} - 44 q^{23} + 18 q^{24} + 6 q^{25} - 37 q^{26} - 4 q^{27} - 13 q^{28} - 11 q^{29} - 30 q^{30} + 21 q^{31} + 82 q^{32} - 22 q^{34} - 13 q^{35} - 238 q^{36} - 4 q^{37} + 41 q^{38} + 118 q^{39} - 79 q^{40} - 12 q^{41} - 63 q^{42} - 44 q^{43} - 34 q^{45} - 31 q^{46} + 38 q^{47} - 76 q^{48} - 197 q^{49} - 14 q^{50} - 7 q^{51} - 31 q^{52} - 6 q^{53} + 17 q^{54} - 11 q^{56} + 60 q^{57} - 80 q^{58} + 10 q^{59} + 103 q^{60} + 34 q^{61} - 32 q^{62} + 19 q^{63} - 139 q^{64} + 24 q^{65} - 2 q^{67} - q^{68} + 46 q^{69} - 47 q^{70} + 19 q^{71} - 96 q^{72} + 20 q^{73} - q^{74} - 59 q^{75} + 130 q^{76} - 65 q^{78} - 11 q^{79} - 81 q^{80} + 752 q^{81} + 64 q^{82} - 57 q^{83} - 16 q^{84} + 26 q^{85} - 31 q^{86} - 48 q^{87} - 64 q^{89} + 191 q^{90} + 44 q^{91} - 70 q^{92} + 21 q^{93} - 70 q^{94} + 46 q^{95} + 170 q^{96} - 67 q^{97} - 112 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3025, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3025, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3025, [\chi]) \cong \)