Properties

Label 462.2.p
Level $462$
Weight $2$
Character orbit 462.p
Rep. character $\chi_{462}(241,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
Newform subspaces $2$
Sturm bound $192$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(192\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(13\)

Dimensions

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

Total New Old
Modular forms 208 32 176
Cusp forms 176 32 144
Eisenstein series 32 0 32

Trace form

\( 32q + 16q^{4} + 24q^{5} + 16q^{9} + O(q^{10}) \) \( 32q + 16q^{4} + 24q^{5} + 16q^{9} - 8q^{11} + 16q^{14} - 8q^{15} - 16q^{16} + 4q^{22} - 8q^{23} + 20q^{25} + 24q^{26} + 12q^{31} + 6q^{33} + 32q^{36} + 28q^{37} - 24q^{38} + 12q^{42} + 8q^{44} + 24q^{45} - 48q^{47} - 12q^{49} + 8q^{56} - 4q^{60} - 32q^{64} - 32q^{67} - 60q^{70} - 112q^{71} - 24q^{75} - 20q^{77} - 24q^{80} - 16q^{81} - 24q^{82} - 24q^{86} + 2q^{88} - 72q^{89} - 16q^{91} - 16q^{92} + 8q^{93} - 16q^{99} + O(q^{100}) \)

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.p.a \(16\) \(3.689\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(12\) \(-6\) \(q-\beta _{11}q^{2}-\beta _{12}q^{3}-\beta _{13}q^{4}+(1+\beta _{8}+\cdots)q^{5}+\cdots\)
462.2.p.b \(16\) \(3.689\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(12\) \(6\) \(q-\beta _{12}q^{2}+\beta _{11}q^{3}+(1+\beta _{13})q^{4}+\cdots\)

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

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