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Properties

Label 2366.2.bb
Level $2366$
Weight $2$
Character orbit 2366.bb
Rep. character $\chi_{2366}(437,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $416$
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.bb (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(728\)

Dimensions

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

Total New Old
Modular forms 1568 416 1152
Cusp forms 1344 416 928
Eisenstein series 224 0 224

Trace form

\( 416 q - 8 q^{7} + 216 q^{9} + O(q^{10}) \) \( 416 q - 8 q^{7} + 216 q^{9} - 12 q^{11} + 8 q^{14} - 32 q^{15} + 208 q^{16} - 16 q^{18} + 36 q^{19} + 16 q^{22} + 4 q^{28} + 80 q^{29} + 12 q^{31} + 84 q^{33} + 80 q^{35} - 24 q^{37} + 72 q^{42} - 12 q^{44} + 12 q^{46} + 36 q^{47} + 48 q^{50} - 24 q^{53} + 36 q^{54} - 16 q^{57} + 8 q^{58} - 16 q^{60} - 24 q^{61} + 60 q^{63} + 8 q^{67} - 24 q^{68} - 8 q^{70} - 40 q^{71} + 16 q^{72} + 12 q^{73} - 40 q^{74} - 64 q^{79} - 288 q^{81} - 128 q^{85} - 4 q^{86} - 48 q^{87} - 108 q^{89} - 4 q^{93} - 144 q^{94} + 8 q^{98} - 88 q^{99} + O(q^{100}) \)

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

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