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Properties

Label 351.2.r
Level $351$
Weight $2$
Character orbit 351.r
Rep. character $\chi_{351}(10,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $24$
Newform subspaces $2$
Sturm bound $84$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 351 = 3^{3} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 351.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(84\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(351, [\chi])\).

Total New Old
Modular forms 96 32 64
Cusp forms 72 24 48
Eisenstein series 24 8 16

Trace form

\( 24 q + 3 q^{2} + 11 q^{4} - 4 q^{10} + 3 q^{11} - 2 q^{13} + 6 q^{14} - 7 q^{16} - 6 q^{17} - 9 q^{19} - 7 q^{22} + 18 q^{23} + 2 q^{25} + 18 q^{29} + 12 q^{31} + 9 q^{32} - 6 q^{34} + 24 q^{35} - 3 q^{37}+ \cdots - 105 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(351, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
351.2.r.a 351.r 117.r $2$ $2.803$ \(\Q(\sqrt{-3}) \) None 117.2.l.a \(3\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2-\zeta_{6})q^{2}+(1-\zeta_{6})q^{4}+(2-\zeta_{6})q^{5}+\cdots\)
351.2.r.b 351.r 117.r $22$ $2.803$ None 117.2.l.b \(0\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(351, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(351, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)