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Properties

Label 783.2.e
Level $783$
Weight $2$
Character orbit 783.e
Rep. character $\chi_{783}(262,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $56$
Newform subspaces $2$
Sturm bound $180$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 783 = 3^{3} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 783.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(180\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(783, [\chi])\).

Total New Old
Modular forms 192 56 136
Cusp forms 168 56 112
Eisenstein series 24 0 24

Trace form

\( 56 q + 2 q^{2} - 28 q^{4} - 2 q^{5} - 2 q^{7} - 12 q^{8} + 6 q^{11} - 2 q^{13} - 2 q^{14} - 28 q^{16} - 4 q^{17} - 8 q^{19} - 8 q^{20} + 6 q^{22} - 4 q^{23} - 22 q^{25} + 24 q^{26} + 16 q^{28} + 6 q^{29}+ \cdots - 172 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(783, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
783.2.e.a 783.e 9.c $22$ $6.252$ None 261.2.e.a \(1\) \(0\) \(-1\) \(7\) $\mathrm{SU}(2)[C_{3}]$
783.2.e.b 783.e 9.c $34$ $6.252$ None 261.2.e.b \(1\) \(0\) \(-1\) \(-9\) $\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{2}^{\mathrm{old}}(783, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(783, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(261, [\chi])\)\(^{\oplus 2}\)