Properties

Label 462.2.i
Level $462$
Weight $2$
Character orbit 462.i
Rep. character $\chi_{462}(67,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $24$
Newform subspaces $7$
Sturm bound $192$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 7 \)
Sturm bound: \(192\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(462, [\chi])\).

Total New Old
Modular forms 208 24 184
Cusp forms 176 24 152
Eisenstein series 32 0 32

Trace form

\( 24q - 12q^{4} - 12q^{9} + O(q^{10}) \) \( 24q - 12q^{4} - 12q^{9} - 12q^{16} + 8q^{19} - 8q^{21} - 16q^{23} - 20q^{25} - 4q^{33} + 24q^{34} - 32q^{35} + 24q^{36} - 12q^{37} + 16q^{38} - 8q^{39} + 64q^{41} + 8q^{42} + 48q^{43} - 8q^{46} + 8q^{47} - 24q^{49} + 32q^{50} - 8q^{51} - 40q^{53} + 32q^{57} - 36q^{58} + 16q^{59} + 8q^{61} + 24q^{64} - 48q^{65} - 8q^{66} - 8q^{67} + 24q^{69} - 40q^{70} + 16q^{73} - 48q^{74} + 8q^{75} - 16q^{76} - 8q^{77} - 16q^{78} - 40q^{79} - 12q^{81} - 16q^{82} + 32q^{83} + 16q^{84} - 48q^{85} + 24q^{87} + 40q^{89} - 24q^{91} + 32q^{92} - 16q^{93} + 16q^{94} - 16q^{95} + 120q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(462, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
462.2.i.a \(2\) \(3.689\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-3\) \(-5\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
462.2.i.b \(2\) \(3.689\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(0\) \(-4\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
462.2.i.c \(2\) \(3.689\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(3\) \(5\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
462.2.i.d \(2\) \(3.689\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(0\) \(4\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
462.2.i.e \(4\) \(3.689\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(2\) \(2\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1-\beta _{2})q^{4}+\cdots\)
462.2.i.f \(6\) \(3.689\) 6.0.1156923.1 None \(-3\) \(-3\) \(0\) \(0\) \(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
462.2.i.g \(6\) \(3.689\) 6.0.21870000.1 None \(-3\) \(3\) \(0\) \(0\) \(q+\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1-\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(462, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(462, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)