Properties

Label 234.2.l
Level $234$
Weight $2$
Character orbit 234.l
Rep. character $\chi_{234}(127,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $3$
Sturm bound $84$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 234.l (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(84\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(234, [\chi])\).

Total New Old
Modular forms 100 12 88
Cusp forms 68 12 56
Eisenstein series 32 0 32

Trace form

\( 12 q + 6 q^{4} + O(q^{10}) \) \( 12 q + 6 q^{4} - 2 q^{10} - 14 q^{13} + 16 q^{14} - 6 q^{16} + 8 q^{17} + 24 q^{19} + 8 q^{23} - 16 q^{25} - 8 q^{26} - 8 q^{29} - 16 q^{35} - 18 q^{37} - 4 q^{40} - 48 q^{41} + 8 q^{43} - 10 q^{49} - 24 q^{50} - 4 q^{52} + 8 q^{56} + 6 q^{58} + 48 q^{59} - 2 q^{61} + 16 q^{62} - 12 q^{64} + 8 q^{65} - 8 q^{68} - 24 q^{71} + 8 q^{74} + 24 q^{76} + 48 q^{77} - 16 q^{79} - 22 q^{82} - 18 q^{85} + 24 q^{89} + 32 q^{91} + 16 q^{92} + 24 q^{94} - 24 q^{95} - 48 q^{97} - 24 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(234, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
234.2.l.a 234.l 13.e $4$ $1.868$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-1+2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
234.2.l.b 234.l 13.e $4$ $1.868$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+3\zeta_{12}^{3}q^{5}+\cdots\)
234.2.l.c 234.l 13.e $4$ $1.868$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(1-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(234, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(234, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)