Properties

Label 336.2.b
Level 336
Weight 2
Character orbit b
Rep. character \(\chi_{336}(223,\cdot)\)
Character field \(\Q\)
Dimension 8
Newforms 4
Sturm bound 128
Trace bound 7

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Defining parameters

Level: \( N \) = \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 336.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 28 \)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(128\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(336, [\chi])\).

Total New Old
Modular forms 76 8 68
Cusp forms 52 8 44
Eisenstein series 24 0 24

Trace form

\(8q \) \(\mathstrut +\mathstrut 8q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut +\mathstrut 8q^{9} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut +\mathstrut 16q^{25} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut -\mathstrut 16q^{49} \) \(\mathstrut -\mathstrut 48q^{53} \) \(\mathstrut +\mathstrut 8q^{57} \) \(\mathstrut -\mathstrut 48q^{65} \) \(\mathstrut +\mathstrut 8q^{81} \) \(\mathstrut -\mathstrut 24q^{85} \) \(\mathstrut +\mathstrut 16q^{93} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(336, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
336.2.b.a \(2\) \(2.683\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(-4\) \(q-q^{3}+(-2-\zeta_{6})q^{7}+q^{9}-2\zeta_{6}q^{11}+\cdots\)
336.2.b.b \(2\) \(2.683\) \(\Q(\sqrt{-6}) \) None \(0\) \(-2\) \(0\) \(2\) \(q-q^{3}+\beta q^{5}+(1-\beta )q^{7}+q^{9}+\beta q^{11}+\cdots\)
336.2.b.c \(2\) \(2.683\) \(\Q(\sqrt{-6}) \) None \(0\) \(2\) \(0\) \(-2\) \(q+q^{3}+\beta q^{5}+(-1+\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
336.2.b.d \(2\) \(2.683\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(4\) \(q+q^{3}+(2+\zeta_{6})q^{7}+q^{9}+2\zeta_{6}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(336, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(336, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)