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Properties

Label 2366.2.bf
Level $2366$
Weight $2$
Character orbit 2366.bf
Rep. character $\chi_{2366}(155,\cdot)$
Character field $\Q(\zeta_{26})$
Dimension $1104$
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.bf (of order \(26\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{26})\)
Sturm bound: \(728\)

Dimensions

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

Total New Old
Modular forms 4416 1104 3312
Cusp forms 4320 1104 3216
Eisenstein series 96 0 96

Trace form

\( 1104 q + 92 q^{4} - 104 q^{9} + O(q^{10}) \) \( 1104 q + 92 q^{4} - 104 q^{9} + 8 q^{10} + 16 q^{13} - 4 q^{14} + 52 q^{15} - 92 q^{16} + 8 q^{17} + 48 q^{22} - 8 q^{23} + 104 q^{25} + 24 q^{27} - 20 q^{29} + 96 q^{30} + 104 q^{31} - 4 q^{35} + 104 q^{36} + 16 q^{38} - 52 q^{39} + 44 q^{40} - 4 q^{42} - 20 q^{43} - 260 q^{45} - 104 q^{47} + 92 q^{49} + 268 q^{51} - 16 q^{52} + 4 q^{53} - 40 q^{55} + 4 q^{56} + 156 q^{57} + 52 q^{58} - 104 q^{60} + 16 q^{61} - 24 q^{62} + 92 q^{64} + 12 q^{65} + 16 q^{66} + 52 q^{67} - 8 q^{68} + 24 q^{74} + 80 q^{75} + 24 q^{77} + 44 q^{78} + 32 q^{79} - 148 q^{81} - 32 q^{82} + 260 q^{83} + 52 q^{85} + 8 q^{87} + 4 q^{88} - 16 q^{90} - 8 q^{91} + 8 q^{92} - 260 q^{93} + 88 q^{94} + 88 q^{95} + O(q^{100}) \)

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

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