Properties

Label 728.2.k
Level $728$
Weight $2$
Character orbit 728.k
Rep. character $\chi_{728}(337,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $2$
Sturm bound $224$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 728.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(224\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(728, [\chi])\).

Total New Old
Modular forms 120 20 100
Cusp forms 104 20 84
Eisenstein series 16 0 16

Trace form

\( 20 q + 16 q^{9} + O(q^{10}) \) \( 20 q + 16 q^{9} + 8 q^{13} + 8 q^{17} - 32 q^{25} + 4 q^{29} + 12 q^{35} - 16 q^{39} - 20 q^{43} - 20 q^{49} + 8 q^{51} - 20 q^{53} - 64 q^{55} - 40 q^{61} + 24 q^{65} + 8 q^{69} + 40 q^{75} + 8 q^{77} + 60 q^{81} + 56 q^{87} + 4 q^{91} + 20 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(728, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
728.2.k.a 728.k 13.b $8$ $5.813$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(-\beta _{1}+\beta _{5})q^{5}-\beta _{5}q^{7}+\cdots\)
728.2.k.b 728.k 13.b $12$ $5.813$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(-\beta _{1}+\beta _{5}+\beta _{7})q^{5}-\beta _{4}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(728, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(728, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(364, [\chi])\)\(^{\oplus 2}\)