Properties

Label 462.2.c
Level $462$
Weight $2$
Character orbit 462.c
Rep. character $\chi_{462}(197,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $2$
Sturm bound $192$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(192\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(17\)

Dimensions

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

Total New Old
Modular forms 104 24 80
Cusp forms 88 24 64
Eisenstein series 16 0 16

Trace form

\( 24q + 8q^{3} + 24q^{4} + O(q^{10}) \) \( 24q + 8q^{3} + 24q^{4} + 8q^{12} + 8q^{15} + 24q^{16} + 16q^{22} - 56q^{25} - 16q^{27} + 24q^{31} + 8q^{34} - 24q^{45} + 8q^{48} - 24q^{49} + 8q^{55} - 16q^{58} + 8q^{60} + 24q^{64} - 32q^{66} + 48q^{67} - 40q^{69} + 8q^{70} - 80q^{75} + 72q^{78} + 8q^{81} - 40q^{82} + 16q^{88} - 48q^{91} - 48q^{93} - 96q^{97} + 56q^{99} + O(q^{100}) \)

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

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

\( S_{2}^{\mathrm{old}}(462, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)