Properties

Label 192.4.c
Level $192$
Weight $4$
Character orbit 192.c
Rep. character $\chi_{192}(191,\cdot)$
Character field $\Q$
Dimension $22$
Newform subspaces $4$
Sturm bound $128$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 192.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(128\)
Trace bound: \(9\)
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 26 82
Cusp forms 84 22 62
Eisenstein series 24 4 20

Trace form

\( 22 q - 2 q^{9} + O(q^{10}) \) \( 22 q - 2 q^{9} - 68 q^{13} - 52 q^{21} - 354 q^{25} + 176 q^{33} - 500 q^{37} + 736 q^{45} - 494 q^{49} + 396 q^{57} - 164 q^{61} + 800 q^{69} - 4 q^{73} + 2150 q^{81} - 256 q^{85} + 284 q^{93} - 1492 q^{97} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
192.4.c.a 192.c 12.b $2$ $11.328$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) 48.4.c.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\zeta_{6}q^{3}-6\zeta_{6}q^{7}-3^{3}q^{9}-70q^{13}+\cdots\)
192.4.c.b 192.c 12.b $4$ $11.328$ \(\Q(\sqrt{3}, \sqrt{-5})\) None 12.4.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{3}+\beta _{2}q^{5}+(\beta _{1}-\beta _{3})q^{7}+(-3+\cdots)q^{9}+\cdots\)
192.4.c.c 192.c 12.b $4$ $11.328$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None 48.4.c.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+\beta _{3}q^{5}-5\beta _{1}q^{7}+(21-\beta _{3})q^{9}+\cdots\)
192.4.c.d 192.c 12.b $12$ $11.328$ 12.0.\(\cdots\).1 None 96.4.c.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{3}+\beta _{8}q^{5}+\beta _{1}q^{7}+(-2+\beta _{5}+\cdots)q^{9}+\cdots\)

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

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