Properties

Label 192.2.c
Level $192$
Weight $2$
Character orbit 192.c
Rep. character $\chi_{192}(191,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $2$
Sturm bound $64$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 192.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(64\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(192, [\chi])\).

Total New Old
Modular forms 44 10 34
Cusp forms 20 6 14
Eisenstein series 24 4 20

Trace form

\( 6q - 2q^{9} + O(q^{10}) \) \( 6q - 2q^{9} + 12q^{13} - 4q^{21} - 2q^{25} - 16q^{33} - 4q^{37} - 32q^{45} + 2q^{49} + 12q^{57} - 20q^{61} + 32q^{69} - 4q^{73} - 10q^{81} + 44q^{93} + 12q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(192, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
192.2.c.a \(2\) \(1.533\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}q^{3}-2\zeta_{6}q^{7}-3q^{9}+2q^{13}+\cdots\)
192.2.c.b \(4\) \(1.533\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{3}-\zeta_{8}^{3}q^{5}+(\zeta_{8}-\zeta_{8}^{2})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(192, [\chi])\) into lower level spaces

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