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Properties

Label 2793.2.em
Level $2793$
Weight $2$
Character orbit 2793.em
Rep. character $\chi_{2793}(52,\cdot)$
Character field $\Q(\zeta_{126})$
Dimension $6732$
Sturm bound $746$

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Defining parameters

Level: \( N \) \(=\) \( 2793 = 3 \cdot 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2793.em (of order \(126\) and degree \(36\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 931 \)
Character field: \(\Q(\zeta_{126})\)
Sturm bound: \(746\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2793, [\chi])\).

Total New Old
Modular forms 13572 6732 6840
Cusp forms 13284 6732 6552
Eisenstein series 288 0 288

Trace form

\( 6732 q - 6 q^{7} + O(q^{10}) \) \( 6732 q - 6 q^{7} - 54 q^{10} - 78 q^{11} + 12 q^{12} + 30 q^{13} - 48 q^{14} + 36 q^{17} + 33 q^{19} + 168 q^{20} - 18 q^{21} + 12 q^{22} - 132 q^{26} - 3 q^{27} - 24 q^{28} + 24 q^{29} + 498 q^{32} + 36 q^{34} - 96 q^{35} + 36 q^{37} + 108 q^{40} - 108 q^{41} - 72 q^{42} + 36 q^{43} - 288 q^{44} + 42 q^{45} + 90 q^{46} + 18 q^{49} + 54 q^{50} - 342 q^{52} - 72 q^{53} + 108 q^{56} - 72 q^{59} - 108 q^{61} + 210 q^{62} - 18 q^{63} - 582 q^{64} + 12 q^{67} - 36 q^{70} + 144 q^{72} + 3 q^{73} + 60 q^{74} + 21 q^{75} - 108 q^{76} + 30 q^{77} - 192 q^{78} + 12 q^{79} + 120 q^{82} - 72 q^{83} + 108 q^{84} - 192 q^{85} - 546 q^{86} + 126 q^{89} - 54 q^{90} + 216 q^{91} + 51 q^{93} + 216 q^{94} + 54 q^{97} - 30 q^{98} + 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2793, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2793, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2793, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(931, [\chi])\)\(^{\oplus 2}\)