Properties

Label 234.6.b
Level $234$
Weight $6$
Character orbit 234.b
Rep. character $\chi_{234}(181,\cdot)$
Character field $\Q$
Dimension $30$
Newform subspaces $5$
Sturm bound $252$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 234.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(252\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(234, [\chi])\).

Total New Old
Modular forms 218 30 188
Cusp forms 202 30 172
Eisenstein series 16 0 16

Trace form

\( 30 q - 480 q^{4} + O(q^{10}) \) \( 30 q - 480 q^{4} - 120 q^{10} - 156 q^{13} + 1752 q^{14} + 7680 q^{16} - 1038 q^{17} - 2160 q^{22} - 4236 q^{23} - 18132 q^{25} - 3048 q^{26} - 3840 q^{29} - 11394 q^{35} + 14640 q^{38} + 1920 q^{40} + 19062 q^{43} - 40320 q^{49} + 2496 q^{52} - 42108 q^{53} - 64320 q^{55} - 28032 q^{56} - 11472 q^{61} - 36864 q^{62} - 122880 q^{64} + 176022 q^{65} + 16608 q^{68} - 10248 q^{74} - 40776 q^{77} + 155844 q^{79} + 75024 q^{82} + 34560 q^{88} + 65094 q^{91} + 67776 q^{92} - 119400 q^{94} - 464340 q^{95} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(234, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
234.6.b.a 234.b 13.b $2$ $37.530$ \(\Q(\sqrt{-1}) \) None 26.6.b.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}-2^{4}q^{4}+34iq^{5}-41iq^{7}+\cdots\)
234.6.b.b 234.b 13.b $2$ $37.530$ \(\Q(\sqrt{-1}) \) None 26.6.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-4iq^{2}-2^{4}q^{4}+51iq^{5}-105iq^{7}+\cdots\)
234.6.b.c 234.b 13.b $6$ $37.530$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 78.6.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-2^{4}q^{4}+(3\beta _{1}-\beta _{3})q^{5}+(14\beta _{1}+\cdots)q^{7}+\cdots\)
234.6.b.d 234.b 13.b $8$ $37.530$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None 78.6.b.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}-2^{4}q^{4}+(-\beta _{3}+\beta _{4})q^{5}+\cdots\)
234.6.b.e 234.b 13.b $12$ $37.530$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 234.6.b.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}-2^{4}q^{4}+(-\beta _{3}+\beta _{4})q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(234, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(234, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)