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Properties

Label 2541.2.bm
Level $2541$
Weight $2$
Character orbit 2541.bm
Rep. character $\chi_{2541}(233,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $2176$
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.bm (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 231 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(704\)

Dimensions

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

Total New Old
Modular forms 3008 2432 576
Cusp forms 2624 2176 448
Eisenstein series 384 256 128

Trace form

\( 2176 q + 3 q^{3} + 262 q^{4} + 20 q^{6} + 20 q^{7} + 9 q^{9} + O(q^{10}) \) \( 2176 q + 3 q^{3} + 262 q^{4} + 20 q^{6} + 20 q^{7} + 9 q^{9} - 24 q^{12} + 40 q^{13} - 12 q^{15} + 206 q^{16} + 5 q^{18} + 10 q^{19} + 25 q^{24} - 202 q^{25} - 6 q^{27} - 10 q^{28} + 35 q^{30} - 256 q^{34} + 28 q^{36} + 6 q^{37} + 45 q^{39} + 120 q^{40} + 6 q^{42} - 16 q^{45} + 50 q^{46} - 94 q^{48} + 48 q^{49} + 45 q^{51} + 10 q^{52} - 60 q^{57} - 28 q^{58} + 87 q^{60} + 50 q^{61} - 60 q^{63} - 224 q^{64} + 32 q^{67} - 78 q^{69} - 68 q^{70} - 55 q^{72} + 70 q^{73} - 49 q^{75} - 340 q^{78} + 90 q^{79} - 31 q^{81} - 10 q^{82} - 125 q^{84} - 160 q^{85} - 30 q^{90} + 192 q^{91} + 30 q^{93} + 210 q^{94} - 135 q^{96} + 40 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2541, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)