Properties

Label 1386.2.cx
Level $1386$
Weight $2$
Character orbit 1386.cx
Rep. character $\chi_{1386}(269,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $256$
Sturm bound $576$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.cx (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

\( 256q - 32q^{4} - 8q^{7} + O(q^{10}) \) \( 256q - 32q^{4} - 8q^{7} - 24q^{10} + 32q^{16} + 24q^{22} - 12q^{28} - 36q^{31} - 8q^{37} + 36q^{40} - 32q^{43} - 16q^{46} - 80q^{49} - 20q^{58} + 64q^{64} + 64q^{67} + 20q^{70} + 48q^{73} - 40q^{79} - 48q^{82} - 128q^{85} + 12q^{88} - 32q^{91} + 72q^{94} + O(q^{100}) \)

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

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