Properties

Label 462.2.g
Level $462$
Weight $2$
Character orbit 462.g
Rep. character $\chi_{462}(419,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $5$
Sturm bound $192$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(192\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\)

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

\( 24q - 24q^{4} + 12q^{7} + 8q^{9} + O(q^{10}) \) \( 24q - 24q^{4} + 12q^{7} + 8q^{9} + 32q^{15} + 24q^{16} - 8q^{18} - 4q^{21} + 8q^{25} - 12q^{28} + 24q^{30} - 8q^{36} + 32q^{37} - 16q^{39} + 32q^{43} + 56q^{46} - 40q^{51} - 32q^{57} - 32q^{60} - 28q^{63} - 24q^{64} - 80q^{67} - 32q^{70} + 8q^{72} - 56q^{79} + 8q^{81} + 4q^{84} - 16q^{85} - 8q^{91} + 16q^{93} + O(q^{100}) \)

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.g.a \(4\) \(3.689\) \(\Q(i, \sqrt{5})\) None \(0\) \(-2\) \(-4\) \(6\) \(q+\beta _{2}q^{2}+(-1-\beta _{1})q^{3}-q^{4}+(-2+\cdots)q^{5}+\cdots\)
462.2.g.b \(4\) \(3.689\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(-4\) \(q-\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots\)
462.2.g.c \(4\) \(3.689\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(8\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{3}q^{3}-q^{4}+\zeta_{12}^{2}q^{6}+\cdots\)
462.2.g.d \(4\) \(3.689\) \(\Q(i, \sqrt{5})\) None \(0\) \(2\) \(4\) \(6\) \(q-\beta _{2}q^{2}+(\beta _{2}+\beta _{3})q^{3}-q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
462.2.g.e \(8\) \(3.689\) 8.0.342102016.5 None \(0\) \(0\) \(0\) \(-4\) \(q+\beta _{1}q^{2}-\beta _{7}q^{3}-q^{4}+(\beta _{4}-\beta _{5})q^{5}+\cdots\)

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

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