↑

Properties

Label 2493.2.h
Level $2493$
Weight $2$
Character orbit 2493.h
Rep. character $\chi_{2493}(991,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $228$
Sturm bound $556$

Related objects

Downloads

Learn more

Defining parameters

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

Dimensions

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

Total New Old
Modular forms 564 232 332
Cusp forms 548 228 320
Eisenstein series 16 4 12

Trace form

\( 228 q + 4 q^{2} + 220 q^{4} + 4 q^{5} + O(q^{10}) \) \( 228 q + 4 q^{2} + 220 q^{4} + 4 q^{5} + 5 q^{10} + 8 q^{11} - 8 q^{13} - 16 q^{14} + 204 q^{16} - 4 q^{17} - 16 q^{19} + 23 q^{20} - 8 q^{22} - 4 q^{23} - 104 q^{25} + 26 q^{26} - 4 q^{28} + 9 q^{29} + 5 q^{31} + 34 q^{32} + 4 q^{34} - 5 q^{35} - 16 q^{37} - 34 q^{38} + 22 q^{40} - 42 q^{41} + 2 q^{43} + 23 q^{44} + 16 q^{46} - 6 q^{47} - 112 q^{49} + 13 q^{50} - 66 q^{52} - 28 q^{53} + 24 q^{55} - 46 q^{56} - 29 q^{58} + 84 q^{59} - 20 q^{61} - 15 q^{62} + 136 q^{64} - 9 q^{65} + 26 q^{67} + 8 q^{68} + 49 q^{70} - 15 q^{71} - 16 q^{73} + 52 q^{74} - 78 q^{76} + 29 q^{77} + 11 q^{79} + 71 q^{80} - 96 q^{82} - 37 q^{83} - 3 q^{85} - 9 q^{86} + 13 q^{88} - 33 q^{89} - 23 q^{91} + 35 q^{92} + 20 q^{94} + 3 q^{95} + 7 q^{97} - 48 q^{98} + O(q^{100}) \)

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

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