Properties

Label 1386.2.co
Level $1386$
Weight $2$
Character orbit 1386.co
Rep. character $\chi_{1386}(107,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $256$
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.co (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 231 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 2432 256 2176
Cusp forms 2176 256 1920
Eisenstein series 256 0 256

Trace form

\( 256q + 32q^{4} + O(q^{10}) \) \( 256q + 32q^{4} + 32q^{16} - 8q^{22} - 48q^{25} + 20q^{28} + 12q^{31} + 64q^{34} - 8q^{37} - 20q^{40} - 80q^{49} + 24q^{55} + 4q^{58} - 160q^{61} - 64q^{64} - 64q^{67} - 12q^{70} - 40q^{73} + 32q^{82} + 160q^{85} + 4q^{88} - 40q^{94} + 64q^{97} + O(q^{100}) \)

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

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