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Properties

Label 2366.2.bx
Level $2366$
Weight $2$
Character orbit 2366.bx
Rep. character $\chi_{2366}(43,\cdot)$
Character field $\Q(\zeta_{78})$
Dimension $2208$
Sturm bound $728$

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Defining parameters

Level: \( N \) \(=\) \( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2366.bx (of order \(78\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{78})\)
Sturm bound: \(728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2366, [\chi])\).

Total New Old
Modular forms 8832 2208 6624
Cusp forms 8640 2208 6432
Eisenstein series 192 0 192

Trace form

\( 2208 q - 92 q^{4} + 92 q^{9} + O(q^{10}) \) \( 2208 q - 92 q^{4} + 92 q^{9} + 4 q^{10} + 12 q^{11} + 8 q^{13} - 8 q^{14} - 40 q^{15} + 92 q^{16} + 4 q^{17} - 48 q^{22} - 4 q^{23} + 184 q^{25} - 24 q^{27} + 8 q^{29} + 348 q^{30} - 104 q^{31} - 24 q^{33} + 4 q^{35} - 92 q^{36} - 12 q^{37} - 16 q^{38} + 100 q^{39} - 44 q^{40} + 36 q^{41} + 4 q^{42} - 16 q^{43} + 200 q^{45} + 12 q^{46} + 572 q^{47} - 92 q^{49} + 12 q^{50} - 220 q^{51} + 4 q^{52} - 64 q^{53} + 36 q^{54} + 4 q^{55} - 4 q^{56} - 156 q^{57} - 76 q^{58} + 104 q^{60} + 8 q^{61} - 12 q^{62} + 12 q^{63} + 184 q^{64} + 24 q^{65} - 16 q^{66} - 40 q^{67} - 4 q^{68} - 36 q^{69} + 12 q^{72} - 36 q^{74} + 40 q^{75} + 4 q^{78} - 32 q^{79} + 136 q^{81} - 16 q^{82} + 520 q^{83} - 12 q^{84} - 112 q^{85} - 92 q^{87} - 4 q^{88} + 16 q^{90} + 20 q^{91} - 8 q^{92} + 212 q^{93} - 112 q^{94} + 164 q^{95} - 48 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2366, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2366, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2366, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1183, [\chi])\)\(^{\oplus 2}\)