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Properties

Label 702.2.bb
Level $702$
Weight $2$
Character orbit 702.bb
Rep. character $\chi_{702}(71,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $56$
Newform subspaces $1$
Sturm bound $252$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 702.bb (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(252\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(702, [\chi])\).

Total New Old
Modular forms 552 56 496
Cusp forms 456 56 400
Eisenstein series 96 0 96

Trace form

\( 56 q + 4 q^{7} + O(q^{10}) \) \( 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73} - 48 q^{74} + 4 q^{76} + 24 q^{77} - 24 q^{79} + 60 q^{83} - 48 q^{86} + 4 q^{91} + 24 q^{92} + 20 q^{97} + 48 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(702, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
702.2.bb.a 702.bb 117.x $56$ $5.605$ None 234.2.y.a \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(702, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(702, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(351, [\chi])\)\(^{\oplus 2}\)