Properties

Label 460.2.i
Level $460$
Weight $2$
Character orbit 460.i
Rep. character $\chi_{460}(137,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $24$
Newform subspaces $2$
Sturm bound $144$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 460.i (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(i)\)
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 156 24 132
Cusp forms 132 24 108
Eisenstein series 24 0 24

Trace form

\( 24q - 4q^{3} + O(q^{10}) \) \( 24q - 4q^{3} + 8q^{13} - 2q^{23} + 24q^{25} + 20q^{27} - 12q^{31} - 4q^{35} - 12q^{41} + 4q^{47} + 36q^{55} + 52q^{71} - 20q^{73} - 56q^{75} - 36q^{77} - 112q^{81} - 16q^{85} - 16q^{87} + 88q^{93} - 24q^{95} + O(q^{100}) \)

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.i.a \(8\) \(3.673\) 8.0.\(\cdots\).3 None \(0\) \(-8\) \(0\) \(0\) \(q+(-1-\beta _{3})q^{3}+(-\beta _{1}+\beta _{6})q^{5}-\beta _{2}q^{7}+\cdots\)
460.2.i.b \(16\) \(3.673\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(4\) \(0\) \(0\) \(q+\beta _{6}q^{3}-\beta _{3}q^{5}+(-\beta _{3}+\beta _{15})q^{7}+\cdots\)

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

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