Properties

Label 462.2.ba
Level $462$
Weight $2$
Character orbit 462.ba
Rep. character $\chi_{462}(19,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $128$
Newform subspaces $2$
Sturm bound $192$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.ba (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 2 \)
Sturm bound: \(192\)
Trace bound: \(5\)
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

\( 128q - 16q^{4} - 24q^{5} + 20q^{7} - 16q^{9} + O(q^{10}) \) \( 128q - 16q^{4} - 24q^{5} + 20q^{7} - 16q^{9} + 8q^{11} + 4q^{14} - 12q^{15} + 16q^{16} + 60q^{17} - 4q^{22} + 8q^{23} - 24q^{26} - 10q^{28} - 40q^{29} + 18q^{31} - 6q^{33} + 40q^{35} - 32q^{36} - 28q^{37} + 24q^{38} + 30q^{40} - 2q^{42} + 12q^{44} - 24q^{45} + 48q^{47} + 72q^{49} + 40q^{51} - 8q^{56} + 10q^{58} + 4q^{60} - 60q^{61} + 20q^{63} + 32q^{64} + 32q^{67} - 60q^{68} - 50q^{70} - 48q^{71} - 180q^{73} - 40q^{74} + 24q^{75} - 80q^{77} - 60q^{79} - 36q^{80} + 16q^{81} - 96q^{82} - 160q^{85} - 36q^{86} - 22q^{88} - 48q^{89} - 124q^{91} + 16q^{92} - 28q^{93} - 20q^{95} + 16q^{99} + O(q^{100}) \)

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.ba.a \(64\) \(3.689\) None \(0\) \(0\) \(-22\) \(4\)
462.2.ba.b \(64\) \(3.689\) None \(0\) \(0\) \(-2\) \(16\)

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

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