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Properties

Label 592.2.t
Level $592$
Weight $2$
Character orbit 592.t
Rep. character $\chi_{592}(31,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $38$
Newform subspaces $4$
Sturm bound $152$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 592 = 2^{4} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 592.t (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 148 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(152\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 164 38 126
Cusp forms 140 38 102
Eisenstein series 24 0 24

Trace form

\( 38 q - 6 q^{5} + 38 q^{9} + O(q^{10}) \) \( 38 q - 6 q^{5} + 38 q^{9} - 14 q^{13} - 6 q^{17} + 6 q^{29} - 8 q^{37} - 6 q^{45} - 54 q^{49} + 8 q^{57} + 38 q^{61} + 24 q^{69} + 38 q^{81} + 30 q^{89} - 64 q^{93} - 2 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.t.a 592.t 148.g $2$ $4.727$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-2\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1+i)q^{5}-3q^{9}+(-1+i)q^{13}+\cdots\)
592.2.t.b 592.t 148.g $4$ $4.727$ \(\Q(i, \sqrt{7})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{3}+(-1+\beta _{1})q^{5}+\beta _{3}q^{7}+4q^{9}+\cdots\)
592.2.t.c 592.t 148.g $4$ $4.727$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{12}^{3}q^{3}+(2-2\zeta_{12})q^{5}-\zeta_{12}^{2}q^{7}+\cdots\)
592.2.t.d 592.t 148.g $28$ $4.727$ None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(592, [\chi]) \cong \)