Properties

Label 462.2.n
Level $462$
Weight $2$
Character orbit 462.n
Rep. character $\chi_{462}(65,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $64$
Newform subspaces $6$
Sturm bound $192$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 231 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 6 \)
Sturm bound: \(192\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\), \(17\)

Dimensions

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

Total New Old
Modular forms 208 64 144
Cusp forms 176 64 112
Eisenstein series 32 0 32

Trace form

\( 64q - 32q^{4} + 8q^{9} + O(q^{10}) \) \( 64q - 32q^{4} + 8q^{9} - 16q^{15} - 32q^{16} - 4q^{22} + 44q^{25} - 24q^{27} - 4q^{31} + 26q^{33} - 8q^{34} - 16q^{36} - 4q^{37} - 24q^{42} - 56q^{45} + 4q^{49} + 84q^{55} - 32q^{58} + 8q^{60} + 64q^{64} + 8q^{66} + 8q^{67} - 64q^{69} + 52q^{70} - 52q^{75} - 48q^{78} - 24q^{81} + 16q^{82} + 2q^{88} - 24q^{91} - 44q^{93} + 32q^{97} - 24q^{99} + O(q^{100}) \)

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.n.a \(4\) \(3.689\) \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(-2\) \(-6\) \(3\) \(3\) \(q-\beta _{2}q^{2}+(-1-\beta _{2})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
462.2.n.b \(4\) \(3.689\) \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(-2\) \(6\) \(-3\) \(-3\) \(q-\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1+\beta _{2})q^{4}+\cdots\)
462.2.n.c \(4\) \(3.689\) \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(2\) \(-6\) \(3\) \(-3\) \(q+(1-\beta _{2})q^{2}+(-2+\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots\)
462.2.n.d \(4\) \(3.689\) \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(2\) \(6\) \(-3\) \(3\) \(q+\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1+\beta _{2})q^{4}+\cdots\)
462.2.n.e \(24\) \(3.689\) None \(-12\) \(0\) \(0\) \(0\)
462.2.n.f \(24\) \(3.689\) None \(12\) \(0\) \(0\) \(0\)

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

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