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Properties

Label 3025.2.be
Level $3025$
Weight $2$
Character orbit 3025.be
Rep. character $\chi_{3025}(276,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $2060$
Sturm bound $660$

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Defining parameters

Level: \( N \) \(=\) \( 3025 = 5^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3025.be (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 121 \)
Character field: \(\Q(\zeta_{11})\)
Sturm bound: \(660\)

Dimensions

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

Total New Old
Modular forms 3360 2120 1240
Cusp forms 3240 2060 1180
Eisenstein series 120 60 60

Trace form

\( 2060 q + 12 q^{2} + 22 q^{3} - 192 q^{4} - 9 q^{6} + 5 q^{7} + 14 q^{8} + 2022 q^{9} + O(q^{10}) \) \( 2060 q + 12 q^{2} + 22 q^{3} - 192 q^{4} - 9 q^{6} + 5 q^{7} + 14 q^{8} + 2022 q^{9} - 20 q^{11} - 3 q^{12} + 20 q^{13} + q^{14} - 222 q^{16} + 23 q^{17} + 77 q^{18} + 3 q^{19} + 6 q^{21} + 54 q^{22} - 9 q^{23} + 16 q^{24} - 53 q^{26} + 100 q^{27} + 3 q^{28} + 17 q^{29} - 55 q^{31} + 18 q^{32} + 43 q^{33} + 41 q^{34} - 311 q^{36} + 40 q^{37} + 61 q^{38} - 112 q^{39} - 31 q^{41} + 42 q^{42} - 3 q^{43} + 9 q^{44} - 3 q^{46} + 7 q^{47} + 48 q^{48} - 173 q^{49} - 53 q^{51} - 129 q^{52} - 87 q^{53} + 72 q^{54} - 162 q^{56} - 33 q^{57} - 88 q^{58} + 43 q^{59} - 27 q^{61} - 66 q^{62} + 160 q^{63} - 256 q^{64} - 17 q^{66} + 38 q^{67} + 25 q^{68} - 60 q^{69} + 11 q^{71} + 171 q^{72} - q^{73} - 13 q^{74} - 3 q^{76} - 127 q^{77} - 48 q^{78} - 11 q^{79} + 1812 q^{81} + 11 q^{82} - 11 q^{83} - 24 q^{84} + 43 q^{86} + 76 q^{87} - 101 q^{88} + 20 q^{89} - 28 q^{91} - 35 q^{92} - q^{93} + 134 q^{94} - 136 q^{96} - 38 q^{97} - 172 q^{98} + 57 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3025, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(605, [\chi])\)\(^{\oplus 2}\)