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Properties

Label 3025.2.j
Level $3025$
Weight $2$
Character orbit 3025.j
Rep. character $\chi_{3025}(81,\cdot)$
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.j (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

\( 1048 q + q^{2} + 7 q^{3} - 253 q^{4} + 4 q^{5} + 34 q^{6} + 4 q^{7} + 3 q^{8} - 239 q^{9} + O(q^{10}) \) \( 1048 q + q^{2} + 7 q^{3} - 253 q^{4} + 4 q^{5} + 34 q^{6} + 4 q^{7} + 3 q^{8} - 239 q^{9} + 12 q^{10} - 6 q^{12} - 7 q^{13} - 2 q^{14} - q^{15} - 231 q^{16} + 12 q^{17} + q^{18} - 15 q^{19} + 25 q^{20} - 14 q^{21} - 24 q^{23} - 22 q^{24} - 14 q^{25} + 18 q^{26} + 16 q^{27} - 13 q^{28} - 11 q^{29} + 25 q^{30} + 21 q^{31} - 28 q^{32} - 22 q^{34} - 18 q^{35} + 882 q^{36} + 96 q^{37} + 51 q^{38} - 7 q^{39} - 14 q^{40} - 12 q^{41} - 93 q^{42} + 86 q^{43} - 124 q^{45} + 14 q^{46} - 27 q^{47} + 29 q^{48} - 222 q^{49} - 4 q^{50} - 7 q^{51} - 26 q^{52} - 66 q^{53} - 18 q^{54} - 46 q^{56} + 50 q^{57} + 15 q^{58} - 10 q^{59} + 48 q^{60} - 11 q^{61} - 122 q^{62} - 51 q^{63} - 239 q^{64} + 4 q^{65} - 62 q^{67} + 39 q^{68} - 4 q^{69} + 73 q^{70} + 39 q^{71} - 11 q^{72} - 55 q^{73} - q^{74} + 16 q^{75} + 100 q^{76} - 120 q^{78} + 134 q^{79} - 26 q^{80} - 208 q^{81} - 36 q^{82} - 2 q^{83} + 144 q^{84} + 46 q^{85} + 69 q^{86} + 62 q^{87} - 39 q^{89} - 39 q^{90} + 59 q^{91} - 205 q^{92} + 151 q^{93} - 10 q^{94} + 91 q^{95} - 5 q^{96} - 102 q^{97} - 57 q^{98} + O(q^{100}) \)

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

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