Properties

Label 462.2.e
Level $462$
Weight $2$
Character orbit 462.e
Rep. character $\chi_{462}(307,\cdot)$
Character field $\Q$
Dimension $16$
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.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q\)
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 104 16 88
Cusp forms 88 16 72
Eisenstein series 16 0 16

Trace form

\( 16q - 16q^{4} - 16q^{9} + O(q^{10}) \) \( 16q - 16q^{4} - 16q^{9} - 16q^{11} - 16q^{14} + 8q^{15} + 16q^{16} + 8q^{22} - 16q^{23} - 32q^{25} + 16q^{36} + 32q^{37} + 16q^{44} - 24q^{49} + 16q^{56} - 8q^{60} - 16q^{64} + 32q^{67} - 24q^{70} + 16q^{71} - 16q^{77} + 16q^{81} - 48q^{86} - 8q^{88} + 40q^{91} + 16q^{92} + 40q^{93} + 16q^{99} + O(q^{100}) \)

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.e.a \(8\) \(3.689\) 8.0.6679465984.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}+(-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
462.2.e.b \(8\) \(3.689\) 8.0.6679465984.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}+(-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)

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

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