Properties

Label 192.4.d
Level $192$
Weight $4$
Character orbit 192.d
Rep. character $\chi_{192}(97,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $3$
Sturm bound $128$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 192.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(128\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(192, [\chi])\).

Total New Old
Modular forms 108 12 96
Cusp forms 84 12 72
Eisenstein series 24 0 24

Trace form

\( 12 q - 108 q^{9} + O(q^{10}) \) \( 12 q - 108 q^{9} - 312 q^{17} - 564 q^{25} - 1416 q^{41} - 132 q^{49} + 336 q^{57} + 4608 q^{65} - 1320 q^{73} + 972 q^{81} + 264 q^{89} + 11496 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(192, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
192.4.d.a 192.d 8.b $4$ $11.328$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3\zeta_{12}q^{3}-3\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}+\cdots\)
192.4.d.b 192.d 8.b $4$ $11.328$ \(\Q(i, \sqrt{11})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3\beta _{1}q^{3}-\beta _{3}q^{5}+\beta _{2}q^{7}-9q^{9}+\cdots\)
192.4.d.c 192.d 8.b $4$ $11.328$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}-7\zeta_{12}^{3}q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(192, [\chi])\) into lower level spaces

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