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Properties

Label 2493.2.bz
Level $2493$
Weight $2$
Character orbit 2493.bz
Rep. character $\chi_{2493}(289,\cdot)$
Character field $\Q(\zeta_{138})$
Dimension $5060$
Sturm bound $556$

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Defining parameters

Level: \( N \) \(=\) \( 2493 = 3^{2} \cdot 277 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2493.bz (of order \(138\) and degree \(44\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 277 \)
Character field: \(\Q(\zeta_{138})\)
Sturm bound: \(556\)

Dimensions

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

Total New Old
Modular forms 12408 5148 7260
Cusp forms 12056 5060 6996
Eisenstein series 352 88 264

Trace form

\( 5060 q + 46 q^{2} + 184 q^{4} + 46 q^{5} - 48 q^{7} + 46 q^{8} + O(q^{10}) \) \( 5060 q + 46 q^{2} + 184 q^{4} + 46 q^{5} - 48 q^{7} + 46 q^{8} - 49 q^{10} + 46 q^{11} - 13 q^{13} + 64 q^{14} - 304 q^{16} + 25 q^{17} - 46 q^{19} - 27 q^{20} - 50 q^{22} - 58 q^{23} - 173 q^{25} + 46 q^{26} - 26 q^{28} - 30 q^{29} - 43 q^{31} - 92 q^{32} - 63 q^{34} + 12 q^{35} + 230 q^{38} - 32 q^{40} + 44 q^{41} - 64 q^{43} + 168 q^{44} + 97 q^{46} + 148 q^{47} + 55 q^{49} + 82 q^{50} - 124 q^{52} - 106 q^{53} - 81 q^{55} + 178 q^{56} - 217 q^{58} - 6 q^{59} + 253 q^{61} + 51 q^{62} + 228 q^{64} + 133 q^{65} - 48 q^{67} - 72 q^{68} + 123 q^{70} + 13 q^{71} - 46 q^{73} + 10 q^{74} - 111 q^{76} + 67 q^{77} - 133 q^{79} + 145 q^{80} - 46 q^{82} + 97 q^{83} - 11 q^{85} + 71 q^{86} - 15 q^{88} + 104 q^{89} - 83 q^{91} + 439 q^{92} - 102 q^{94} + 174 q^{95} - 67 q^{97} - 471 q^{98} + O(q^{100}) \)

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

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