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Properties

Label 2541.2.i
Level $2541$
Weight $2$
Character orbit 2541.i
Rep. character $\chi_{2541}(1453,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $290$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(704\)

Dimensions

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

Total New Old
Modular forms 752 290 462
Cusp forms 656 290 366
Eisenstein series 96 0 96

Trace form

\( 290 q + 2 q^{2} - q^{3} - 142 q^{4} - 2 q^{5} - 4 q^{6} + 3 q^{7} - 24 q^{8} - 145 q^{9} + O(q^{10}) \) \( 290 q + 2 q^{2} - q^{3} - 142 q^{4} - 2 q^{5} - 4 q^{6} + 3 q^{7} - 24 q^{8} - 145 q^{9} + 8 q^{10} - 2 q^{12} - 14 q^{13} - 14 q^{14} + 4 q^{15} - 144 q^{16} + 2 q^{18} + 7 q^{19} + 56 q^{20} + 4 q^{21} - 8 q^{23} - 151 q^{25} + 22 q^{26} + 2 q^{27} - 8 q^{29} + 12 q^{30} - 13 q^{31} + 36 q^{32} - 46 q^{35} + 284 q^{36} + q^{37} - 10 q^{38} - q^{39} + 12 q^{40} + 52 q^{41} - 10 q^{42} + 2 q^{43} - 2 q^{45} + 32 q^{46} + 18 q^{47} - 8 q^{48} - 37 q^{49} - 60 q^{50} - 8 q^{51} + 10 q^{52} - 28 q^{53} + 2 q^{54} - 24 q^{56} - 14 q^{57} + 12 q^{58} + 12 q^{59} + 16 q^{60} + 2 q^{61} + 52 q^{62} - 3 q^{63} + 256 q^{64} - 42 q^{65} + 5 q^{67} - 36 q^{68} + 32 q^{69} - 16 q^{70} + 28 q^{71} + 12 q^{72} + 27 q^{73} - 42 q^{74} - 15 q^{75} - 124 q^{76} - 20 q^{78} - 15 q^{79} + 8 q^{80} - 145 q^{81} - 20 q^{82} + 20 q^{83} + 50 q^{84} - 8 q^{85} + 38 q^{86} + 16 q^{87} + 32 q^{89} - 16 q^{90} + 111 q^{91} - 80 q^{92} + 43 q^{93} + 40 q^{94} - 18 q^{95} + 12 q^{96} + 76 q^{97} - 16 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2541, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(847, [\chi])\)\(^{\oplus 2}\)