Properties

Label 168.2.j
Level 168
Weight 2
Character orbit j
Rep. character \(\chi_{168}(155,\cdot)\)
Character field \(\Q\)
Dimension 24
Newforms 4
Sturm bound 64
Trace bound 2

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Defining parameters

Level: \( N \) = \( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 168.j (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 24 \)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(64\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(168, [\chi])\).

Total New Old
Modular forms 36 24 12
Cusp forms 28 24 4
Eisenstein series 8 0 8

Trace form

\(24q \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 6q^{12} \) \(\mathstrut -\mathstrut 12q^{16} \) \(\mathstrut +\mathstrut 8q^{18} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 24q^{25} \) \(\mathstrut -\mathstrut 24q^{27} \) \(\mathstrut -\mathstrut 8q^{28} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 24q^{34} \) \(\mathstrut +\mathstrut 12q^{36} \) \(\mathstrut -\mathstrut 20q^{40} \) \(\mathstrut -\mathstrut 10q^{42} \) \(\mathstrut +\mathstrut 32q^{43} \) \(\mathstrut -\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 6q^{48} \) \(\mathstrut -\mathstrut 24q^{49} \) \(\mathstrut +\mathstrut 44q^{52} \) \(\mathstrut -\mathstrut 10q^{54} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut -\mathstrut 24q^{58} \) \(\mathstrut +\mathstrut 20q^{60} \) \(\mathstrut +\mathstrut 52q^{64} \) \(\mathstrut +\mathstrut 40q^{66} \) \(\mathstrut -\mathstrut 32q^{67} \) \(\mathstrut -\mathstrut 12q^{70} \) \(\mathstrut -\mathstrut 56q^{75} \) \(\mathstrut -\mathstrut 28q^{76} \) \(\mathstrut +\mathstrut 44q^{78} \) \(\mathstrut +\mathstrut 8q^{81} \) \(\mathstrut +\mathstrut 24q^{82} \) \(\mathstrut +\mathstrut 14q^{84} \) \(\mathstrut -\mathstrut 32q^{90} \) \(\mathstrut +\mathstrut 48q^{94} \) \(\mathstrut +\mathstrut 2q^{96} \) \(\mathstrut +\mathstrut 64q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(168, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
168.2.j.a \(4\) \(1.341\) \(\Q(i, \sqrt{5})\) None \(-4\) \(-2\) \(4\) \(0\) \(q+(-1-\beta _{2})q^{2}+(\beta _{1}+\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
168.2.j.b \(4\) \(1.341\) \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{2}+(1-\zeta_{8}^{2})q^{3}+2q^{4}+2\zeta_{8}^{3}q^{5}+\cdots\)
168.2.j.c \(4\) \(1.341\) \(\Q(i, \sqrt{5})\) None \(4\) \(-2\) \(-4\) \(0\) \(q+(1+\beta _{2})q^{2}+(-\beta _{2}-\beta _{3})q^{3}+2\beta _{2}q^{4}+\cdots\)
168.2.j.d \(12\) \(1.341\) 12.0.\(\cdots\).2 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{2}-\beta _{6}q^{3}+(-\beta _{2}-\beta _{3})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(168, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(168, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)