Properties

Label 462.2.j
Level $462$
Weight $2$
Character orbit 462.j
Rep. character $\chi_{462}(169,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $48$
Newform subspaces $8$
Sturm bound $192$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.j (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 8 \)
Sturm bound: \(192\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 416 48 368
Cusp forms 352 48 304
Eisenstein series 64 0 64

Trace form

\( 48q - 12q^{4} - 12q^{9} + O(q^{10}) \) \( 48q - 12q^{4} - 12q^{9} + 32q^{11} + 8q^{13} - 16q^{15} - 12q^{16} - 16q^{17} - 16q^{19} + 16q^{21} - 4q^{22} + 16q^{23} + 24q^{25} - 8q^{26} - 16q^{30} - 16q^{31} - 16q^{33} - 16q^{34} - 12q^{36} + 16q^{37} - 8q^{38} - 16q^{39} - 16q^{41} + 80q^{43} - 8q^{44} - 16q^{47} - 12q^{49} + 48q^{50} - 24q^{51} + 8q^{52} + 56q^{53} + 40q^{55} + 32q^{57} - 24q^{58} + 56q^{59} + 24q^{60} - 24q^{61} + 48q^{62} - 12q^{64} - 80q^{65} + 24q^{66} - 96q^{67} - 16q^{68} + 24q^{69} - 8q^{70} + 8q^{71} - 40q^{73} - 32q^{75} - 16q^{76} - 16q^{77} + 8q^{79} - 12q^{81} - 48q^{82} - 64q^{83} - 4q^{84} - 12q^{85} - 40q^{86} - 32q^{87} - 4q^{88} - 24q^{92} - 4q^{93} - 48q^{94} - 32q^{95} - 16q^{97} - 8q^{99} + O(q^{100}) \)

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.j.a \(4\) \(3.689\) \(\Q(\zeta_{10})\) None \(-1\) \(-1\) \(3\) \(1\) \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
462.2.j.b \(4\) \(3.689\) \(\Q(\zeta_{10})\) None \(-1\) \(1\) \(-1\) \(-1\) \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
462.2.j.c \(4\) \(3.689\) \(\Q(\zeta_{10})\) None \(1\) \(-1\) \(5\) \(1\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+\cdots\)
462.2.j.d \(4\) \(3.689\) \(\Q(\zeta_{10})\) None \(1\) \(1\) \(-3\) \(-1\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)
462.2.j.e \(8\) \(3.689\) 8.0.484000000.9 None \(-2\) \(-2\) \(4\) \(-2\) \(q+\beta _{2}q^{2}+(-1-\beta _{2}-\beta _{3}+\beta _{5})q^{3}+\cdots\)
462.2.j.f \(8\) \(3.689\) 8.0.64000000.1 None \(-2\) \(2\) \(-6\) \(2\) \(q-\beta _{6}q^{2}+(1-\beta _{2}+\beta _{4}-\beta _{6})q^{3}-\beta _{2}q^{4}+\cdots\)
462.2.j.g \(8\) \(3.689\) 8.0.324000000.3 None \(2\) \(-2\) \(0\) \(-2\) \(q-\beta _{2}q^{2}+\beta _{6}q^{3}+\beta _{4}q^{4}+(-\beta _{1}-\beta _{5}+\cdots)q^{5}+\cdots\)
462.2.j.h \(8\) \(3.689\) 8.0.\(\cdots\).8 None \(2\) \(2\) \(-2\) \(2\) \(q-\beta _{3}q^{2}-\beta _{2}q^{3}+(-1-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(462, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)