Properties

Label 192.2.k
Level 192
Weight 2
Character orbit k
Rep. character \(\chi_{192}(47,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 12
Newforms 1
Sturm bound 64
Trace bound 0

Related objects

Downloads

Learn more about

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: \(\Q(i)\)
Newforms: \( 1 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(192, [\chi])\) into irreducible Hecke orbits

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

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