Properties

Label 192.5.e
Level $192$
Weight $5$
Character orbit 192.e
Rep. character $\chi_{192}(65,\cdot)$
Character field $\Q$
Dimension $30$
Newform subspaces $8$
Sturm bound $160$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 192.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(160\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(192, [\chi])\).

Total New Old
Modular forms 140 34 106
Cusp forms 116 30 86
Eisenstein series 24 4 20

Trace form

\( 30 q - 2 q^{9} + O(q^{10}) \) \( 30 q - 2 q^{9} + 356 q^{13} + 164 q^{21} - 2754 q^{25} + 1152 q^{33} + 2084 q^{37} - 5376 q^{45} + 6170 q^{49} - 1284 q^{57} - 12060 q^{61} + 8960 q^{69} - 4 q^{73} + 1246 q^{81} + 8704 q^{85} + 12260 q^{93} - 6084 q^{97} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(192, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
192.5.e.a 192.e 3.b $1$ $19.847$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(-9\) \(0\) \(-94\) $\mathrm{U}(1)[D_{2}]$ \(q-9q^{3}-94q^{7}+3^{4}q^{9}-146q^{13}+\cdots\)
192.5.e.b 192.e 3.b $1$ $19.847$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(9\) \(0\) \(94\) $\mathrm{U}(1)[D_{2}]$ \(q+9q^{3}+94q^{7}+3^{4}q^{9}-146q^{13}+\cdots\)
192.5.e.c 192.e 3.b $2$ $19.847$ \(\Q(\sqrt{-2}) \) None \(0\) \(-6\) \(0\) \(-52\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-3+\beta )q^{3}+2\beta q^{5}-26q^{7}+(-63+\cdots)q^{9}+\cdots\)
192.5.e.d 192.e 3.b $2$ $19.847$ \(\Q(\sqrt{-2}) \) None \(0\) \(6\) \(0\) \(52\) $\mathrm{SU}(2)[C_{2}]$ \(q+(3-\beta )q^{3}+2\beta q^{5}+26q^{7}+(-63+\cdots)q^{9}+\cdots\)
192.5.e.e 192.e 3.b $4$ $19.847$ \(\Q(\sqrt{-2}, \sqrt{13})\) None \(0\) \(-4\) \(0\) \(-24\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{1})q^{3}+(2\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots\)
192.5.e.f 192.e 3.b $4$ $19.847$ \(\Q(\sqrt{-2}, \sqrt{13})\) None \(0\) \(4\) \(0\) \(24\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta _{1})q^{3}+(2\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots\)
192.5.e.g 192.e 3.b $8$ $19.847$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{3}+\beta _{1}q^{5}-\beta _{4}q^{7}+(-11+2\beta _{1}+\cdots)q^{9}+\cdots\)
192.5.e.h 192.e 3.b $8$ $19.847$ 8.0.3317760000.8 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(\beta _{1}+\beta _{4})q^{7}+(-3+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(192, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(192, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)