Properties

Label 234.2.b
Level $234$
Weight $2$
Character orbit 234.b
Rep. character $\chi_{234}(181,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $84$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 234.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(84\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 50 4 46
Cusp forms 34 4 30
Eisenstein series 16 0 16

Trace form

\( 4 q - 4 q^{4} + 2 q^{10} - 2 q^{13} + 2 q^{14} + 4 q^{16} - 2 q^{17} + 4 q^{23} - 6 q^{25} + 2 q^{26} + 20 q^{29} - 26 q^{35} - 24 q^{38} - 2 q^{40} + 6 q^{43} + 2 q^{49} + 2 q^{52} + 24 q^{53} - 2 q^{56}+ \cdots + 12 q^{95}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
234.2.b.a 234.b 13.b $2$ $1.868$ \(\Q(\sqrt{-1}) \) None 78.2.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{2}-q^{4}+2 i q^{5}+2 i q^{7}-i q^{8}+\cdots\)
234.2.b.b 234.b 13.b $2$ $1.868$ \(\Q(\sqrt{-1}) \) None 26.2.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{2}-q^{4}-3 i q^{5}-3 i q^{7}-i q^{8}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(234, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)