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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

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

Display 100 coefficients 10 coefficients

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

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