Properties

Label 462.2.y
Level $462$
Weight $2$
Character orbit 462.y
Rep. character $\chi_{462}(25,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $128$
Newform subspaces $4$
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.y (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{15})\)
Newform subspaces: \( 4 \)
Sturm bound: \(192\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 832 128 704
Cusp forms 704 128 576
Eisenstein series 128 0 128

Trace form

\( 128q + 16q^{4} + 8q^{5} + 8q^{6} + 8q^{7} + 16q^{9} + O(q^{10}) \) \( 128q + 16q^{4} + 8q^{5} + 8q^{6} + 8q^{7} + 16q^{9} + 36q^{10} + 8q^{11} + 16q^{13} + 4q^{14} + 12q^{15} + 16q^{16} + 12q^{17} - 16q^{20} - 4q^{22} + 8q^{23} - 4q^{24} + 40q^{25} + 8q^{26} + 22q^{28} + 24q^{29} - 8q^{30} - 6q^{31} + 2q^{33} + 32q^{34} + 8q^{35} - 32q^{36} + 20q^{37} + 8q^{38} - 14q^{40} - 24q^{41} + 14q^{42} - 16q^{43} - 12q^{44} + 8q^{45} + 88q^{47} + 8q^{49} - 24q^{51} - 8q^{52} + 16q^{53} + 16q^{54} + 12q^{55} + 8q^{56} + 16q^{57} - 2q^{58} - 32q^{59} + 4q^{60} + 20q^{61} - 96q^{62} + 20q^{63} - 32q^{64} - 96q^{65} - 96q^{67} + 12q^{68} - 40q^{69} - 66q^{70} - 144q^{71} - 32q^{73} - 16q^{74} + 8q^{75} - 80q^{76} - 64q^{77} - 16q^{79} - 12q^{80} + 16q^{81} - 24q^{82} - 208q^{83} - 96q^{85} - 36q^{86} + 4q^{87} - 18q^{88} - 80q^{89} + 8q^{90} - 36q^{91} - 16q^{92} + 28q^{93} - 56q^{94} - 12q^{95} - 4q^{96} - 24q^{97} - 48q^{98} - 16q^{99} + O(q^{100}) \)

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.y.a \(24\) \(3.689\) None \(-3\) \(-3\) \(5\) \(11\)
462.2.y.b \(24\) \(3.689\) None \(3\) \(3\) \(5\) \(-5\)
462.2.y.c \(40\) \(3.689\) None \(-5\) \(5\) \(1\) \(9\)
462.2.y.d \(40\) \(3.689\) None \(5\) \(-5\) \(-3\) \(-7\)

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

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