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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
231.2.i.a \(2\) \(1.845\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(-4\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
231.2.i.b \(2\) \(1.845\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(-4\) \(-4\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
231.2.i.c \(2\) \(1.845\) \(\Q(\sqrt{-3}) \) None \(2\) \(1\) \(0\) \(5\) \(q+2\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
231.2.i.d \(4\) \(1.845\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(-2\) \(4\) \(4\) \(q+(1+\beta _{1}+\beta _{2})q^{2}+\beta _{2}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
231.2.i.e \(8\) \(1.845\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-2\) \(-4\) \(-4\) \(2\) \(q-\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
231.2.i.f \(10\) \(1.845\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(-2\) \(5\) \(4\) \(-1\) \(q-\beta _{3}q^{2}+(1+\beta _{2})q^{3}+(-2-2\beta _{2}+\cdots)q^{4}+\cdots\)

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

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