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Properties

Label 3025.2.n
Level $3025$
Weight $2$
Character orbit 3025.n
Rep. character $\chi_{3025}(1219,\cdot)$
Character field $\Q(\zeta_{10})$
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.n (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
Character field: \(\Q(\zeta_{10})\)
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

\( 1048 q + 15 q^{3} - 1010 q^{4} + 3 q^{5} + 3 q^{6} - 15 q^{7} + 253 q^{9} + O(q^{10}) \) \( 1048 q + 15 q^{3} - 1010 q^{4} + 3 q^{5} + 3 q^{6} - 15 q^{7} + 253 q^{9} - 70 q^{12} + 5 q^{13} - q^{14} + 3 q^{15} + 922 q^{16} + 10 q^{17} - 5 q^{18} + 30 q^{19} - q^{20} + 11 q^{21} - 40 q^{23} - 22 q^{24} - 37 q^{25} + 49 q^{26} + 45 q^{27} + 95 q^{28} + 54 q^{29} - 11 q^{30} + 11 q^{31} - 26 q^{34} + 38 q^{35} - 231 q^{36} + 10 q^{37} - 23 q^{39} - 22 q^{40} + 29 q^{41} + 25 q^{42} - 44 q^{45} - 7 q^{46} + 180 q^{48} + 231 q^{49} - 18 q^{50} + 19 q^{51} + 15 q^{52} + 105 q^{53} - 13 q^{54} - 29 q^{56} + 50 q^{57} - 15 q^{59} - 150 q^{60} + 8 q^{61} - 10 q^{62} - 30 q^{63} - 806 q^{64} - 60 q^{65} - 50 q^{67} - 65 q^{68} - 10 q^{69} + 33 q^{70} - 7 q^{71} - 100 q^{72} - 10 q^{73} - 5 q^{74} + 84 q^{75} - 50 q^{76} - 135 q^{78} - 11 q^{79} - 184 q^{80} - 151 q^{81} - 130 q^{82} - 95 q^{83} + 52 q^{85} + 58 q^{86} + 10 q^{87} - 24 q^{89} - 113 q^{90} + 58 q^{91} + 80 q^{92} + 55 q^{93} - 29 q^{94} - 48 q^{95} + 122 q^{96} - 95 q^{97} + 40 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3025, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 2}\)