Properties

Label 1386.2.bq
Level $1386$
Weight $2$
Character orbit 1386.bq
Rep. character $\chi_{1386}(125,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $128$
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.bq (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 231 \)
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 128 1088
Cusp forms 1088 128 960
Eisenstein series 128 0 128

Trace form

\( 128q + 32q^{4} + 8q^{7} + O(q^{10}) \) \( 128q + 32q^{4} + 8q^{7} - 32q^{16} - 24q^{25} + 12q^{28} + 32q^{37} + 32q^{43} + 16q^{46} + 8q^{49} - 40q^{58} + 32q^{64} + 128q^{67} + 4q^{70} - 80q^{79} + 8q^{85} + 32q^{91} + O(q^{100}) \)

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

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