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Properties

Label 2493.2.be
Level $2493$
Weight $2$
Character orbit 2493.be
Rep. character $\chi_{2493}(19,\cdot)$
Character field $\Q(\zeta_{23})$
Dimension $2530$
Sturm bound $556$

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Defining parameters

Level: \( N \) \(=\) \( 2493 = 3^{2} \cdot 277 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2493.be (of order \(23\) and degree \(22\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 277 \)
Character field: \(\Q(\zeta_{23})\)
Sturm bound: \(556\)

Dimensions

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

Total New Old
Modular forms 6204 2574 3630
Cusp forms 6028 2530 3498
Eisenstein series 176 44 132

Trace form

\( 2530 q + 24 q^{2} - 134 q^{4} + 27 q^{5} - 19 q^{7} + 20 q^{8} + O(q^{10}) \) \( 2530 q + 24 q^{2} - 134 q^{4} + 27 q^{5} - 19 q^{7} + 20 q^{8} - 21 q^{10} + 31 q^{11} - 67 q^{13} + 25 q^{14} - 126 q^{16} + 31 q^{17} - 17 q^{19} - 84 q^{20} - 25 q^{22} - 61 q^{23} - 128 q^{25} + 43 q^{26} - 11 q^{28} - 51 q^{29} - 29 q^{31} + 156 q^{32} - 19 q^{34} + 44 q^{35} + 17 q^{37} - 85 q^{38} - q^{40} + 23 q^{41} - 23 q^{43} - 100 q^{44} - 174 q^{46} - 23 q^{47} - 126 q^{49} + 12 q^{50} + 223 q^{52} + 118 q^{53} - 80 q^{55} - 125 q^{56} - 196 q^{58} + 29 q^{59} + 31 q^{61} + 29 q^{62} - 104 q^{64} - 85 q^{65} - 29 q^{67} + 122 q^{68} - 175 q^{70} + 17 q^{71} - 35 q^{73} - 9 q^{74} - 128 q^{76} + 25 q^{77} + 69 q^{79} - 5 q^{80} - 5 q^{82} + 25 q^{83} - 17 q^{85} + 65 q^{86} + 23 q^{88} + 30 q^{89} + 91 q^{91} + 389 q^{92} + 83 q^{94} + 28 q^{95} - 15 q^{97} + 149 q^{98} + O(q^{100}) \)

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

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