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Properties

Label 192.5.b
Level $192$
Weight $5$
Character orbit 192.b
Rep. character $\chi_{192}(31,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $3$
Sturm bound $160$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 192.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(160\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 140 16 124
Cusp forms 116 16 100
Eisenstein series 24 0 24

Trace form

\( 16 q + 432 q^{9} + O(q^{10}) \) \( 16 q + 432 q^{9} - 1440 q^{17} - 4016 q^{25} - 4320 q^{41} - 8496 q^{49} - 7488 q^{57} - 16128 q^{65} + 23200 q^{73} + 11664 q^{81} - 18720 q^{89} + 73952 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.b.a 192.b 8.d $4$ $19.847$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3\zeta_{12}q^{3}+7\zeta_{12}^{2}q^{5}-29\zeta_{12}^{3}q^{7}+\cdots\)
192.5.b.b 192.b 8.d $4$ $19.847$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}+\zeta_{12}^{3}q^{7}+\cdots\)
192.5.b.c 192.b 8.d $8$ $19.847$ 8.0.\(\cdots\).10 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3\beta _{1}q^{3}+(-2\beta _{2}+\beta _{3})q^{5}+(5\beta _{4}+\cdots)q^{7}+\cdots\)

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

\( S_{5}^{\mathrm{old}}(192, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)