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Properties

Label 1116.2.bb
Level $1116$
Weight $2$
Character orbit 1116.bb
Rep. character $\chi_{1116}(161,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $20$
Newform subspaces $2$
Sturm bound $384$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1116 = 2^{2} \cdot 3^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1116.bb (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 93 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(384\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1116, [\chi])\).

Total New Old
Modular forms 408 20 388
Cusp forms 360 20 340
Eisenstein series 48 0 48

Trace form

\( 20 q + 8 q^{7} + O(q^{10}) \) \( 20 q + 8 q^{7} + 6 q^{13} - 2 q^{19} + 6 q^{25} - 20 q^{31} - 6 q^{37} - 18 q^{43} - 2 q^{49} + 8 q^{67} + 42 q^{73} - 36 q^{79} + 100 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1116, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1116.2.bb.a 1116.bb 93.g $4$ $8.911$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None 1116.2.bb.a \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{6}]$ \(q-2\beta _{1}q^{7}+(\beta _{2}-\beta _{3})q^{11}+(1+\beta _{1}+\cdots)q^{13}+\cdots\)
1116.2.bb.b 1116.bb 93.g $16$ $8.911$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 1116.2.bb.b \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{2}+\beta _{8}-\beta _{9}-\beta _{11})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1116, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1116, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(93, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(186, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(279, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(372, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(558, [\chi])\)\(^{\oplus 2}\)