Properties

Label 592.2.g
Level $592$
Weight $2$
Character orbit 592.g
Rep. character $\chi_{592}(369,\cdot)$
Character field $\Q$
Dimension $18$
Newform subspaces $4$
Sturm bound $152$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 592 = 2^{4} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 592.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(152\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(592, [\chi])\).

Total New Old
Modular forms 82 20 62
Cusp forms 70 18 52
Eisenstein series 12 2 10

Trace form

\( 18 q + 4 q^{7} + 14 q^{9} + O(q^{10}) \) \( 18 q + 4 q^{7} + 14 q^{9} - 8 q^{11} - 8 q^{21} - 18 q^{25} + 12 q^{27} - 8 q^{33} - 2 q^{37} - 8 q^{41} - 20 q^{47} - 6 q^{49} + 4 q^{53} + 48 q^{63} + 8 q^{65} + 20 q^{67} - 20 q^{71} + 16 q^{73} - 4 q^{75} - 24 q^{77} + 2 q^{81} + 12 q^{83} + 16 q^{85} + 8 q^{95} - 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(592, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
592.2.g.a 592.g 37.b $2$ $4.727$ \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}-\zeta_{6}q^{5}-q^{7}-2q^{9}-3q^{11}+\cdots\)
592.2.g.b 592.g 37.b $2$ $4.727$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+iq^{5}-3q^{7}-2q^{9}+3q^{11}+\cdots\)
592.2.g.c 592.g 37.b $4$ $4.727$ \(\Q(i, \sqrt{21})\) None \(0\) \(2\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{3})q^{3}-\beta _{1}q^{5}+2q^{7}+(3-\beta _{3})q^{9}+\cdots\)
592.2.g.d 592.g 37.b $10$ $4.727$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-2\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}-\beta _{7}q^{5}+\beta _{3}q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(592, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(592, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(148, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(296, [\chi])\)\(^{\oplus 2}\)