Properties

Label 460.2.m
Level $460$
Weight $2$
Character orbit 460.m
Rep. character $\chi_{460}(41,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $80$
Newform subspaces $2$
Sturm bound $144$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 460.m (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Newform subspaces: \( 2 \)
Sturm bound: \(144\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(460, [\chi])\).

Total New Old
Modular forms 780 80 700
Cusp forms 660 80 580
Eisenstein series 120 0 120

Trace form

\( 80q + 2q^{5} - 4q^{9} + O(q^{10}) \) \( 80q + 2q^{5} - 4q^{9} - 4q^{13} + 22q^{17} + 22q^{19} + 78q^{21} - 6q^{23} - 8q^{25} + 42q^{27} + 8q^{29} + 32q^{31} - 20q^{35} + 16q^{37} - 32q^{39} - 54q^{41} - 68q^{43} - 64q^{45} + 24q^{47} - 52q^{49} - 116q^{51} - 28q^{53} - 44q^{55} + 50q^{57} - 4q^{59} + 60q^{61} + 86q^{63} + 8q^{65} + 52q^{67} + 12q^{69} - 18q^{71} + 44q^{73} + 82q^{77} - 4q^{79} + 60q^{81} + 14q^{83} - 2q^{85} - 112q^{87} - 20q^{89} + 12q^{91} + 4q^{93} - 16q^{95} - 40q^{97} - 140q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(460, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
460.2.m.a \(30\) \(3.673\) None \(0\) \(0\) \(-3\) \(1\)
460.2.m.b \(50\) \(3.673\) None \(0\) \(0\) \(5\) \(-1\)

Decomposition of \(S_{2}^{\mathrm{old}}(460, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(460, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 2}\)