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Properties

Label 2493.2.k
Level $2493$
Weight $2$
Character orbit 2493.k
Rep. character $\chi_{2493}(1225,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $230$
Sturm bound $556$

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Defining parameters

Level: \( N \) \(=\) \( 2493 = 3^{2} \cdot 277 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2493.k (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 277 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(556\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2493, [\chi])\).

Total New Old
Modular forms 564 234 330
Cusp forms 548 230 318
Eisenstein series 16 4 12

Trace form

\( 230 q - 230 q^{4} + 2 q^{7} + O(q^{10}) \) \( 230 q - 230 q^{4} + 2 q^{7} + 3 q^{10} - 10 q^{13} - 18 q^{14} + 258 q^{16} + 21 q^{17} + 27 q^{20} + 4 q^{22} + 12 q^{23} + 127 q^{25} - 20 q^{28} - 16 q^{29} - 3 q^{31} + 17 q^{34} + 57 q^{35} - 14 q^{40} + 2 q^{41} + 18 q^{43} + 39 q^{44} + 18 q^{46} - 10 q^{47} - 101 q^{49} - 36 q^{50} + 32 q^{52} - 9 q^{53} - 34 q^{55} + 6 q^{56} - 36 q^{58} + 52 q^{59} - 5 q^{62} - 274 q^{64} + 51 q^{65} + 2 q^{67} + 3 q^{68} - 31 q^{70} + 33 q^{71} + 36 q^{74} - 50 q^{76} - 21 q^{77} - 5 q^{79} - 99 q^{80} - 51 q^{83} - 35 q^{85} - 25 q^{86} - 31 q^{88} - 12 q^{89} - 101 q^{91} - 71 q^{92} - 36 q^{94} - 105 q^{95} + 21 q^{97} - 81 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2493, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2493, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2493, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(277, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(831, [\chi])\)\(^{\oplus 2}\)