Properties

Label 1386.2.bs
Level $1386$
Weight $2$
Character orbit 1386.bs
Rep. character $\chi_{1386}(811,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $160$
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.bs (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 1216 160 1056
Cusp forms 1088 160 928
Eisenstein series 128 0 128

Trace form

\( 160q + 40q^{4} + 10q^{7} + O(q^{10}) \) \( 160q + 40q^{4} + 10q^{7} - 12q^{11} + 2q^{14} - 40q^{16} + 4q^{22} + 16q^{23} + 12q^{25} + 10q^{28} - 20q^{29} + 40q^{35} + 40q^{37} - 8q^{44} + 24q^{49} - 16q^{53} + 8q^{56} - 16q^{58} + 40q^{64} + 112q^{67} - 4q^{70} - 8q^{71} + 40q^{74} + 68q^{77} + 60q^{79} + 40q^{85} + 28q^{86} + 16q^{88} - 20q^{91} + 44q^{92} - 60q^{95} + O(q^{100}) \)

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

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