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Properties

Label 2366.2.n
Level $2366$
Weight $2$
Character orbit 2366.n
Rep. character $\chi_{2366}(1689,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $208$
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.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(728\)

Dimensions

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

Total New Old
Modular forms 784 208 576
Cusp forms 672 208 464
Eisenstein series 112 0 112

Trace form

\( 208 q + 104 q^{4} - 116 q^{9} + O(q^{10}) \) \( 208 q + 104 q^{4} - 116 q^{9} + 4 q^{10} - 104 q^{16} + 12 q^{17} + 8 q^{22} - 16 q^{23} + 104 q^{25} + 24 q^{27} - 24 q^{29} + 20 q^{30} + 24 q^{35} - 232 q^{36} + 16 q^{38} - 4 q^{40} - 20 q^{42} + 8 q^{43} + 36 q^{49} + 36 q^{51} + 56 q^{55} - 12 q^{56} + 40 q^{61} - 16 q^{62} - 208 q^{64} + 16 q^{66} - 12 q^{68} - 24 q^{69} + 24 q^{74} - 52 q^{75} - 68 q^{77} + 12 q^{79} - 152 q^{81} - 8 q^{82} + 4 q^{88} - 64 q^{90} - 32 q^{92} - 24 q^{94} + 8 q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2366, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1183, [\chi])\)\(^{\oplus 2}\)