Properties

Label 192.2.k
Level $192$
Weight $2$
Character orbit 192.k
Rep. character $\chi_{192}(47,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $12$
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.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
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 20 60
Cusp forms 48 12 36
Eisenstein series 32 8 24

Trace form

\( 12q + 2q^{3} + 8q^{7} + O(q^{10}) \) \( 12q + 2q^{3} + 8q^{7} - 4q^{13} + 12q^{19} - 8q^{21} - 10q^{27} - 4q^{33} - 4q^{37} - 20q^{39} - 12q^{43} - 12q^{45} - 20q^{49} - 24q^{51} - 24q^{55} + 12q^{61} - 28q^{67} + 4q^{69} + 34q^{75} - 4q^{81} + 32q^{85} + 60q^{87} + 56q^{91} + 28q^{93} - 8q^{97} + 52q^{99} + O(q^{100}) \)

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.k.a \(12\) \(1.533\) 12.0.\(\cdots\).2 None \(0\) \(2\) \(0\) \(8\) \(q-\beta _{10}q^{3}+\beta _{7}q^{5}+(1-\beta _{11})q^{7}+(\beta _{3}+\cdots)q^{9}+\cdots\)

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

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