Properties

Label 168.2.i
Level 168
Weight 2
Character orbit i
Rep. character \(\chi_{168}(125,\cdot)\)
Character field \(\Q\)
Dimension 28
Newforms 5
Sturm bound 64
Trace bound 4

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Defining parameters

Level: \( N \) = \( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 168.i (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 168 \)
Character field: \(\Q\)
Newforms: \( 5 \)
Sturm bound: \(64\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\)

Dimensions

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

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

Trace form

\(28q \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 4q^{16} \) \(\mathstrut +\mathstrut 12q^{18} \) \(\mathstrut -\mathstrut 32q^{22} \) \(\mathstrut -\mathstrut 20q^{25} \) \(\mathstrut -\mathstrut 12q^{28} \) \(\mathstrut -\mathstrut 4q^{30} \) \(\mathstrut -\mathstrut 40q^{36} \) \(\mathstrut -\mathstrut 16q^{39} \) \(\mathstrut +\mathstrut 12q^{42} \) \(\mathstrut +\mathstrut 32q^{46} \) \(\mathstrut +\mathstrut 4q^{49} \) \(\mathstrut -\mathstrut 16q^{57} \) \(\mathstrut -\mathstrut 16q^{58} \) \(\mathstrut +\mathstrut 44q^{60} \) \(\mathstrut -\mathstrut 36q^{63} \) \(\mathstrut -\mathstrut 52q^{64} \) \(\mathstrut +\mathstrut 48q^{70} \) \(\mathstrut +\mathstrut 12q^{72} \) \(\mathstrut +\mathstrut 68q^{78} \) \(\mathstrut +\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 12q^{81} \) \(\mathstrut +\mathstrut 36q^{84} \) \(\mathstrut +\mathstrut 8q^{88} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.i.a \(4\) \(1.341\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(-4\) \(0\) \(-8\) \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{3}+(1+\beta _{3})q^{4}+\cdots\)
168.2.i.b \(4\) \(1.341\) \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-6}) \) \(0\) \(0\) \(0\) \(4\) \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+2q^{4}+2\beta _{2}q^{5}+\cdots\)
168.2.i.c \(4\) \(1.341\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(4\) \(0\) \(-8\) \(q+\beta _{1}q^{2}+(1-\beta _{2})q^{3}+(1+\beta _{3})q^{4}+\cdots\)
168.2.i.d \(8\) \(1.341\) 8.0.\(\cdots\).11 \(\Q(\sqrt{-14}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}-\beta _{1}q^{3}-2q^{4}+(\beta _{6}-\beta _{7})q^{5}+\cdots\)
168.2.i.e \(8\) \(1.341\) 8.0.3317760000.1 None \(0\) \(0\) \(0\) \(8\) \(q+\beta _{5}q^{2}+(-\beta _{4}-\beta _{6})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)