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Properties

Label 2366.2.i
Level $2366$
Weight $2$
Character orbit 2366.i
Rep. character $\chi_{2366}(2127,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $200$
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.i (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(i)\)
Sturm bound: \(728\)

Dimensions

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

Total New Old
Modular forms 784 200 584
Cusp forms 672 200 472
Eisenstein series 112 0 112

Trace form

\( 200 q - 8 q^{7} - 184 q^{9} + O(q^{10}) \) \( 200 q - 8 q^{7} - 184 q^{9} - 8 q^{14} - 16 q^{15} - 200 q^{16} - 8 q^{18} - 4 q^{21} - 16 q^{22} - 8 q^{28} + 16 q^{29} - 8 q^{35} + 8 q^{37} + 24 q^{50} - 16 q^{57} - 8 q^{58} + 16 q^{60} + 40 q^{63} + 96 q^{67} + 44 q^{70} + 64 q^{71} + 8 q^{72} + 16 q^{74} - 32 q^{79} - 8 q^{81} - 4 q^{84} + 56 q^{85} - 56 q^{86} - 112 q^{93} - 32 q^{98} + 16 q^{99} + O(q^{100}) \)

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

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