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Properties

Label 2366.2.cd
Level $2366$
Weight $2$
Character orbit 2366.cd
Rep. character $\chi_{2366}(41,\cdot)$
Character field $\Q(\zeta_{156})$
Dimension $5760$
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.cd (of order \(156\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1183 \)
Character field: \(\Q(\zeta_{156})\)
Sturm bound: \(728\)

Dimensions

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

Total New Old
Modular forms 17664 5760 11904
Cusp forms 17280 5760 11520
Eisenstein series 384 0 384

Trace form

\( 5760 q + 4 q^{7} - 232 q^{9} + O(q^{10}) \) \( 5760 q + 4 q^{7} - 232 q^{9} + 16 q^{15} - 240 q^{16} + 8 q^{18} + 24 q^{21} + 4 q^{28} + 8 q^{29} - 80 q^{30} - 16 q^{35} + 24 q^{36} + 48 q^{37} - 136 q^{39} - 12 q^{42} + 24 q^{43} + 24 q^{44} - 24 q^{49} + 32 q^{53} + 12 q^{56} + 8 q^{57} - 40 q^{58} + 8 q^{60} - 200 q^{63} + 40 q^{65} + 352 q^{67} + 200 q^{70} + 32 q^{71} - 32 q^{72} + 216 q^{74} - 8 q^{78} - 48 q^{79} + 200 q^{81} - 24 q^{84} - 240 q^{85} - 304 q^{86} - 8 q^{91} - 16 q^{92} + 56 q^{93} - 120 q^{95} + 32 q^{98} - 88 q^{99} + O(q^{100}) \)

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

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