Properties

Label 192.3.e
Level $192$
Weight $3$
Character orbit 192.e
Rep. character $\chi_{192}(65,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $6$
Sturm bound $96$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 192.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(96\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

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

Total New Old
Modular forms 76 18 58
Cusp forms 52 14 38
Eisenstein series 24 4 20

Trace form

\( 14q - 2q^{9} + O(q^{10}) \) \( 14q - 2q^{9} - 12q^{13} + 20q^{21} - 34q^{25} + 84q^{37} + 10q^{49} + 60q^{57} - 76q^{61} - 256q^{69} - 4q^{73} - 146q^{81} - 256q^{85} + 308q^{93} + 28q^{97} + O(q^{100}) \)

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.e.a \(1\) \(5.232\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(-3\) \(0\) \(-2\) \(q-3q^{3}-2q^{7}+9q^{9}+22q^{13}+26q^{19}+\cdots\)
192.3.e.b \(1\) \(5.232\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(3\) \(0\) \(2\) \(q+3q^{3}+2q^{7}+9q^{9}+22q^{13}-26q^{19}+\cdots\)
192.3.e.c \(2\) \(5.232\) \(\Q(\sqrt{-2}) \) None \(0\) \(-2\) \(0\) \(-12\) \(q+(-1+\beta )q^{3}-2\beta q^{5}-6q^{7}+(-7+\cdots)q^{9}+\cdots\)
192.3.e.d \(2\) \(5.232\) \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(12\) \(q+(1+\beta )q^{3}+2\beta q^{5}+6q^{7}+(-7+2\beta )q^{9}+\cdots\)
192.3.e.e \(4\) \(5.232\) \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{2}q^{5}+(-2\beta _{1}+\beta _{3})q^{7}+\cdots\)
192.3.e.f \(4\) \(5.232\) \(\Q(\sqrt{-2}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{3})q^{3}+\beta _{2}q^{5}+(\beta _{1}+2\beta _{3})q^{7}+\cdots\)

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

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