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Properties

Label 592.3.k
Level $592$
Weight $3$
Character orbit 592.k
Rep. character $\chi_{592}(401,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $74$
Newform subspaces $8$
Sturm bound $228$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 592 = 2^{4} \cdot 37 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 592.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 8 \)
Sturm bound: \(228\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(592, [\chi])\).

Total New Old
Modular forms 316 78 238
Cusp forms 292 74 218
Eisenstein series 24 4 20

Trace form

\( 74 q + 2 q^{5} + 4 q^{7} - 214 q^{9} + O(q^{10}) \) \( 74 q + 2 q^{5} + 4 q^{7} - 214 q^{9} - 14 q^{13} - 64 q^{15} + 2 q^{17} + 34 q^{19} - 30 q^{23} - 6 q^{29} + 66 q^{31} + 32 q^{33} + 52 q^{35} - 2 q^{37} + 32 q^{39} + 178 q^{43} - 94 q^{45} - 284 q^{47} + 462 q^{49} + 64 q^{51} - 4 q^{53} - 48 q^{55} + 64 q^{57} + 2 q^{59} - 102 q^{61} + 484 q^{63} + 16 q^{69} - 28 q^{71} - 32 q^{75} - 270 q^{79} + 554 q^{81} + 4 q^{83} + 352 q^{87} - 214 q^{89} - 380 q^{91} - 80 q^{93} - 150 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(592, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
592.3.k.a 592.k 37.d $2$ $16.131$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-12\) \(-10\) $\mathrm{SU}(2)[C_{4}]$ \(q-iq^{3}+(-6+6i)q^{5}-5q^{7}+8q^{9}+\cdots\)
592.3.k.b 592.k 37.d $2$ $16.131$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(6\) \(-6\) $\mathrm{SU}(2)[C_{4}]$ \(q+3iq^{3}+(3-3i)q^{5}-3q^{7}+3iq^{11}+\cdots\)
592.3.k.c 592.k 37.d $2$ $16.131$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(6\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q-4iq^{3}+(3-3i)q^{5}+4q^{7}-7q^{9}+\cdots\)
592.3.k.d 592.k 37.d $4$ $16.131$ \(\Q(i, \sqrt{65})\) None \(0\) \(0\) \(-6\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{3}+(-2-\beta _{1}+\beta _{2})q^{5}+(3-\beta _{1}+\cdots)q^{7}+\cdots\)
592.3.k.e 592.k 37.d $12$ $16.131$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(-6\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{5}q^{3}+(-1-\beta _{6}+\beta _{11})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
592.3.k.f 592.k 37.d $14$ $16.131$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{3}+(1+\beta _{4}-\beta _{9})q^{5}+\beta _{5}q^{7}+\cdots\)
592.3.k.g 592.k 37.d $18$ $16.131$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(0\) \(0\) \(-2\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{3}-\beta _{11}q^{5}+\beta _{4}q^{7}+(-2+\beta _{2}+\cdots)q^{9}+\cdots\)
592.3.k.h 592.k 37.d $20$ $16.131$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(4\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{3}-\beta _{17}q^{5}-\beta _{4}q^{7}+(-4-\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(592, [\chi])\) into lower level spaces

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