Properties

Label 462.2.k
Level $462$
Weight $2$
Character orbit 462.k
Rep. character $\chi_{462}(89,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $56$
Newform subspaces $7$
Sturm bound $192$
Trace bound $15$

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Defining parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.k (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 7 \)
Sturm bound: \(192\)
Trace bound: \(15\)
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 56 152
Cusp forms 176 56 120
Eisenstein series 32 0 32

Trace form

\( 56q + 28q^{4} + 16q^{7} + 4q^{9} + O(q^{10}) \) \( 56q + 28q^{4} + 16q^{7} + 4q^{9} - 8q^{15} - 28q^{16} + 8q^{18} - 24q^{19} + 16q^{21} - 12q^{24} - 36q^{25} + 8q^{28} + 24q^{31} + 8q^{36} - 12q^{37} - 20q^{39} + 36q^{42} + 48q^{45} + 16q^{46} - 40q^{49} + 4q^{51} - 24q^{52} - 36q^{54} + 8q^{57} + 12q^{58} - 4q^{60} - 56q^{63} - 56q^{64} + 32q^{70} - 8q^{72} + 48q^{73} - 36q^{75} - 20q^{81} + 24q^{82} - 4q^{84} + 16q^{85} - 36q^{87} - 16q^{91} - 28q^{93} - 48q^{94} - 12q^{96} + O(q^{100}) \)

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.k.a \(4\) \(3.689\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(8\) \(q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
462.2.k.b \(4\) \(3.689\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(8\) \(q+\zeta_{12}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
462.2.k.c \(4\) \(3.689\) \(\Q(\zeta_{12})\) None \(0\) \(6\) \(0\) \(2\) \(q+\zeta_{12}q^{2}+(2-\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
462.2.k.d \(8\) \(3.689\) \(\Q(\zeta_{24})\) None \(0\) \(-12\) \(0\) \(4\) \(q+(-\zeta_{24}+\zeta_{24}^{3})q^{2}+(-1-\zeta_{24}^{2}+\cdots)q^{3}+\cdots\)
462.2.k.e \(8\) \(3.689\) \(\Q(\zeta_{24})\) None \(0\) \(4\) \(-4\) \(0\) \(q+(-\zeta_{24}^{2}+\zeta_{24}^{6})q^{2}+(-\zeta_{24}-\zeta_{24}^{2}+\cdots)q^{3}+\cdots\)
462.2.k.f \(8\) \(3.689\) \(\Q(\zeta_{24})\) None \(0\) \(8\) \(4\) \(0\) \(q+(\zeta_{24}^{2}-\zeta_{24}^{6})q^{2}+(1-\zeta_{24}^{3}-\zeta_{24}^{6}+\cdots)q^{3}+\cdots\)
462.2.k.g \(20\) \(3.689\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(-6\) \(0\) \(-6\) \(q-\beta _{7}q^{2}-\beta _{12}q^{3}-\beta _{3}q^{4}+(2\beta _{6}+\beta _{7}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(462, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)