Properties

Label 192.3.g
Level $192$
Weight $3$
Character orbit 192.g
Rep. character $\chi_{192}(127,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $3$
Sturm bound $96$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 192.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(96\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(192, [\chi])\).

Total New Old
Modular forms 76 8 68
Cusp forms 52 8 44
Eisenstein series 24 0 24

Trace form

\( 8q - 24q^{9} + O(q^{10}) \) \( 8q - 24q^{9} - 16q^{13} - 16q^{17} + 48q^{21} + 88q^{25} + 32q^{29} - 176q^{37} - 80q^{41} - 56q^{49} + 160q^{53} + 144q^{61} + 128q^{65} - 96q^{69} - 48q^{73} - 320q^{77} + 72q^{81} + 448q^{85} + 80q^{89} - 144q^{93} - 176q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(192, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
192.3.g.a \(2\) \(5.232\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-12\) \(0\) \(q-\zeta_{6}q^{3}-6q^{5}+4\zeta_{6}q^{7}-3q^{9}+12\zeta_{6}q^{11}+\cdots\)
192.3.g.b \(2\) \(5.232\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(4\) \(0\) \(q-\zeta_{6}q^{3}+2q^{5}-4\zeta_{6}q^{7}-3q^{9}-4\zeta_{6}q^{11}+\cdots\)
192.3.g.c \(4\) \(5.232\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(8\) \(0\) \(q-\zeta_{12}^{2}q^{3}+(2-\zeta_{12}^{3})q^{5}+(-\zeta_{12}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(192, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(192, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)