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

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

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
462.2.i.a 462.i 7.c $2$ $3.689$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-3\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
462.2.i.b 462.i 7.c $2$ $3.689$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
462.2.i.c 462.i 7.c $2$ $3.689$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(3\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
462.2.i.d 462.i 7.c $2$ $3.689$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
462.2.i.e 462.i 7.c $4$ $3.689$ \(\Q(\sqrt{-3}, \sqrt{7})\) None \(2\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1-\beta _{2})q^{4}+\cdots\)
462.2.i.f 462.i 7.c $6$ $3.689$ 6.0.1156923.1 None \(-3\) \(-3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
462.2.i.g 462.i 7.c $6$ $3.689$ 6.0.21870000.1 None \(-3\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1-\beta _{2})q^{4}+\cdots\)

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

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