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Properties

Label 592.2.o
Level $592$
Weight $2$
Character orbit 592.o
Rep. character $\chi_{592}(149,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $144$
Newform subspaces $1$
Sturm bound $152$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 592 = 2^{4} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 592.o (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(152\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 156 144 12
Cusp forms 148 144 4
Eisenstein series 8 0 8

Trace form

\( 144 q - 12 q^{6} - 12 q^{8} - 4 q^{10} + 4 q^{12} + 16 q^{14} - 16 q^{15} - 8 q^{16} - 16 q^{19} + 16 q^{20} - 8 q^{22} + 8 q^{24} + 20 q^{26} + 24 q^{27} - 4 q^{28} + 24 q^{30} + 24 q^{31} - 20 q^{32}+ \cdots + 80 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
592.2.o.a 592.o 16.e $144$ $4.727$ None 592.2.o.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(592, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)