Properties

Label 1386.2.bx
Level $1386$
Weight $2$
Character orbit 1386.bx
Rep. character $\chi_{1386}(37,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $320$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.bx (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1386, [\chi])\).

Total New Old
Modular forms 2432 320 2112
Cusp forms 2176 320 1856
Eisenstein series 256 0 256

Trace form

\( 320q + 40q^{4} - 4q^{5} - 10q^{7} + O(q^{10}) \) \( 320q + 40q^{4} - 4q^{5} - 10q^{7} - 12q^{10} - 8q^{11} - 8q^{13} - 2q^{14} + 40q^{16} - 14q^{17} + 8q^{20} + 8q^{22} + 8q^{23} + 52q^{25} - 16q^{26} - 2q^{28} + 4q^{29} - 6q^{31} + 32q^{34} + 26q^{35} - 16q^{37} - 4q^{38} - 2q^{40} + 80q^{41} + 8q^{43} + 2q^{44} - 12q^{46} - 44q^{47} + 50q^{49} - 32q^{50} + 4q^{52} - 12q^{55} - 4q^{56} + 16q^{58} + 36q^{59} + 62q^{61} + 80q^{62} - 80q^{64} + 40q^{65} - 14q^{68} + 18q^{70} + 136q^{71} + 34q^{73} + 8q^{74} + 40q^{76} + 58q^{77} + 50q^{79} + 6q^{80} + 12q^{82} + 128q^{83} - 12q^{85} + 10q^{86} + 6q^{88} + 60q^{89} + 102q^{91} + 44q^{92} + 28q^{94} + 86q^{95} - 60q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1386, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1386, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1386, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(693, [\chi])\)\(^{\oplus 2}\)