Properties

Label 336.2.k
Level 336
Weight 2
Character orbit k
Rep. character \(\chi_{336}(209,\cdot)\)
Character field \(\Q\)
Dimension 14
Newforms 3
Sturm bound 128
Trace bound 1

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Defining parameters

Level: \( N \) = \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 336.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 21 \)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(128\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 76 18 58
Cusp forms 52 14 38
Eisenstein series 24 4 20

Trace form

\( 14q + 4q^{7} - 2q^{9} + O(q^{10}) \) \( 14q + 4q^{7} - 2q^{9} + 8q^{15} - 2q^{21} - 6q^{25} - 4q^{37} - 16q^{39} + 32q^{43} - 2q^{49} - 4q^{57} - 20q^{63} - 16q^{67} - 8q^{79} - 18q^{81} - 16q^{85} - 24q^{91} + 20q^{93} - 64q^{99} + O(q^{100}) \)

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.k.a \(2\) \(2.683\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{6}q^{3}+(-2-\zeta_{6})q^{7}-3q^{9}-4\zeta_{6}q^{13}+\cdots\)
336.2.k.b \(4\) \(2.683\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(4\) \(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{5}+(1-\beta _{1}-\beta _{3})q^{7}+\cdots\)
336.2.k.c \(8\) \(2.683\) 8.0.342102016.5 None \(0\) \(0\) \(0\) \(4\) \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(1+\beta _{5})q^{7}+(-\beta _{5}+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(336, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)