Properties

Label 462.2.u
Level $462$
Weight $2$
Character orbit 462.u
Rep. character $\chi_{462}(13,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $64$
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.u (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{10})\)
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 416 64 352
Cusp forms 352 64 288
Eisenstein series 64 0 64

Trace form

\( 64q + 16q^{4} - 20q^{7} + 16q^{9} + O(q^{10}) \) \( 64q + 16q^{4} - 20q^{7} + 16q^{9} + 16q^{11} - 4q^{14} + 12q^{15} - 16q^{16} - 8q^{22} + 16q^{23} + 12q^{25} + 10q^{28} + 40q^{29} + 20q^{35} - 16q^{36} - 32q^{37} - 10q^{42} + 24q^{44} + 24q^{49} + 80q^{51} - 16q^{56} + 20q^{58} + 8q^{60} - 20q^{63} + 16q^{64} - 32q^{67} - 46q^{70} - 96q^{71} - 80q^{74} - 64q^{77} - 120q^{79} - 16q^{81} - 20q^{85} - 72q^{86} - 32q^{88} - 80q^{91} - 16q^{92} - 20q^{93} - 40q^{95} - 16q^{99} + O(q^{100}) \)

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.u.a \(32\) \(3.689\) None \(0\) \(0\) \(-10\) \(-10\)
462.2.u.b \(32\) \(3.689\) None \(0\) \(0\) \(10\) \(-10\)

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

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