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Properties

Label 2541.2.j
Level $2541$
Weight $2$
Character orbit 2541.j
Rep. character $\chi_{2541}(148,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $432$
Sturm bound $704$

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Defining parameters

Level: \( N \) \(=\) \( 2541 = 3 \cdot 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2541.j (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(704\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2541, [\chi])\).

Total New Old
Modular forms 1504 432 1072
Cusp forms 1312 432 880
Eisenstein series 192 0 192

Trace form

\( 432 q - 4 q^{2} - 112 q^{4} - 4 q^{7} + 8 q^{8} - 108 q^{9} + O(q^{10}) \) \( 432 q - 4 q^{2} - 112 q^{4} - 4 q^{7} + 8 q^{8} - 108 q^{9} - 16 q^{10} - 16 q^{12} + 4 q^{13} + 6 q^{14} - 8 q^{15} - 76 q^{16} - 8 q^{17} + 6 q^{18} - 8 q^{19} + 60 q^{20} + 16 q^{21} + 48 q^{23} - 84 q^{25} + 44 q^{26} - 2 q^{28} - 16 q^{29} + 8 q^{30} - 28 q^{31} - 88 q^{32} - 56 q^{34} - 112 q^{36} + 28 q^{37} - 12 q^{38} - 32 q^{39} - 4 q^{40} - 8 q^{41} + 48 q^{43} + 6 q^{46} + 16 q^{48} - 108 q^{49} + 64 q^{50} - 24 q^{51} + 68 q^{52} + 52 q^{53} - 36 q^{56} + 8 q^{57} - 62 q^{58} + 4 q^{59} + 24 q^{60} - 32 q^{62} - 4 q^{63} - 96 q^{64} - 40 q^{65} - 80 q^{67} - 88 q^{68} + 12 q^{69} - 32 q^{70} - 12 q^{71} - 2 q^{72} - 8 q^{73} + 28 q^{74} + 32 q^{75} + 16 q^{76} + 56 q^{78} - 36 q^{79} - 216 q^{80} - 108 q^{81} - 44 q^{82} + 88 q^{83} - 12 q^{84} + 12 q^{85} - 150 q^{86} - 40 q^{87} + 160 q^{89} + 24 q^{90} - 74 q^{92} + 20 q^{93} + 20 q^{94} + 128 q^{95} + 60 q^{96} - 52 q^{97} - 4 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2541, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2541, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2541, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(363, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(847, [\chi])\)\(^{\oplus 2}\)