Properties

Label 231.2.i
Level $231$
Weight $2$
Character orbit 231.i
Rep. character $\chi_{231}(67,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $28$
Newform subspaces $6$
Sturm bound $64$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 231 = 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 231.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 6 \)
Sturm bound: \(64\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(231, [\chi])\).

Total New Old
Modular forms 72 28 44
Cusp forms 56 28 28
Eisenstein series 16 0 16

Trace form

\( 28 q + 2 q^{3} - 16 q^{4} + 2 q^{7} + 24 q^{8} - 14 q^{9} + O(q^{10}) \) \( 28 q + 2 q^{3} - 16 q^{4} + 2 q^{7} + 24 q^{8} - 14 q^{9} - 12 q^{10} + 4 q^{12} + 12 q^{13} - 4 q^{14} - 28 q^{16} - 6 q^{19} - 32 q^{20} - 8 q^{21} + 8 q^{23} - 10 q^{25} - 4 q^{26} - 4 q^{27} - 8 q^{28} - 16 q^{30} + 22 q^{31} - 44 q^{32} + 4 q^{33} + 24 q^{34} + 48 q^{35} + 32 q^{36} - 2 q^{37} + 12 q^{38} + 2 q^{39} - 12 q^{40} - 32 q^{41} + 12 q^{42} - 12 q^{43} - 8 q^{44} - 32 q^{46} - 28 q^{47} + 16 q^{48} + 22 q^{49} + 64 q^{50} + 8 q^{51} - 8 q^{52} + 36 q^{53} - 32 q^{55} + 24 q^{56} + 12 q^{57} + 4 q^{58} - 32 q^{59} - 8 q^{60} + 8 q^{61} - 88 q^{62} + 2 q^{63} + 88 q^{64} + 40 q^{65} + 8 q^{66} - 22 q^{67} + 36 q^{68} - 24 q^{69} + 24 q^{70} + 16 q^{71} - 12 q^{72} - 30 q^{73} + 48 q^{74} + 6 q^{75} + 120 q^{76} + 4 q^{77} - 8 q^{78} + 14 q^{79} - 16 q^{80} - 14 q^{81} - 32 q^{83} - 52 q^{84} + 8 q^{85} - 36 q^{86} - 12 q^{87} + 12 q^{88} - 20 q^{89} + 24 q^{90} - 10 q^{91} + 80 q^{92} + 2 q^{93} - 52 q^{94} + 16 q^{95} - 20 q^{96} - 128 q^{97} + 12 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(231, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
231.2.i.a 231.i 7.c $2$ $1.845$ \(\Q(\sqrt{-3}) \) None 231.2.i.a \(-1\) \(1\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
231.2.i.b 231.i 7.c $2$ $1.845$ \(\Q(\sqrt{-3}) \) None 231.2.i.b \(1\) \(1\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
231.2.i.c 231.i 7.c $2$ $1.845$ \(\Q(\sqrt{-3}) \) None 231.2.i.c \(2\) \(1\) \(0\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
231.2.i.d 231.i 7.c $4$ $1.845$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 231.2.i.d \(2\) \(-2\) \(4\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{2})q^{2}+\beta _{2}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
231.2.i.e 231.i 7.c $8$ $1.845$ 8.0.\(\cdots\).5 None 231.2.i.e \(-2\) \(-4\) \(-4\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
231.2.i.f 231.i 7.c $10$ $1.845$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None 231.2.i.f \(-2\) \(5\) \(4\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{3}q^{2}+(1+\beta _{2})q^{3}+(-2-2\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(231, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(231, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)