Properties

Label 364.2.g
Level $364$
Weight $2$
Character orbit 364.g
Rep. character $\chi_{364}(337,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $1$
Sturm bound $112$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 364 = 2^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 364.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(112\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(364, [\chi])\).

Total New Old
Modular forms 62 8 54
Cusp forms 50 8 42
Eisenstein series 12 0 12

Trace form

\( 8 q + 8 q^{9} + O(q^{10}) \) \( 8 q + 8 q^{9} + 2 q^{13} + 4 q^{17} - 6 q^{23} + 2 q^{25} + 12 q^{27} - 2 q^{29} + 6 q^{35} - 6 q^{43} - 8 q^{49} - 8 q^{51} + 22 q^{53} - 20 q^{55} + 8 q^{61} - 6 q^{65} - 20 q^{69} - 20 q^{75} - 26 q^{79} - 24 q^{81} - 32 q^{87} - 10 q^{91} - 18 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(364, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
364.2.g.a 364.g 13.b $8$ $2.907$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(-\beta _{3}-\beta _{4})q^{5}+\beta _{3}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(364, [\chi])\) into lower level spaces

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