Properties

Label 192.2.j
Level $192$
Weight $2$
Character orbit 192.j
Rep. character $\chi_{192}(49,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $8$
Newform subspaces $1$
Sturm bound $64$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 192.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(64\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 80 8 72
Cusp forms 48 8 40
Eisenstein series 32 0 32

Trace form

\( 8q + O(q^{10}) \) \( 8q + 8q^{11} + 8q^{15} + 8q^{19} - 16q^{29} - 24q^{31} - 24q^{35} - 16q^{37} + 8q^{43} - 8q^{49} - 8q^{51} + 16q^{53} - 32q^{59} + 16q^{61} - 8q^{63} - 16q^{65} + 16q^{67} + 16q^{69} - 16q^{75} + 16q^{77} + 24q^{79} - 8q^{81} + 40q^{83} - 16q^{85} + 8q^{91} + 48q^{95} + 8q^{99} + O(q^{100}) \)

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.j.a \(8\) \(1.533\) 8.0.18939904.2 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}+(-\beta _{3}+\beta _{5})q^{5}+(\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots\)

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

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