Properties

Label 336.2.bj
Level 336
Weight 2
Character orbit bj
Rep. character \(\chi_{336}(95,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 32
Newforms 7
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.bj (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 84 \)
Character field: \(\Q(\zeta_{6})\)
Newforms: \( 7 \)
Sturm bound: \(128\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(13\), \(19\)

Dimensions

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

Total New Old
Modular forms 152 32 120
Cusp forms 104 32 72
Eisenstein series 48 0 48

Trace form

\( 32q + O(q^{10}) \) \( 32q + 8q^{13} - 12q^{21} + 28q^{25} + 4q^{37} - 12q^{45} + 8q^{49} - 48q^{57} - 8q^{61} - 96q^{69} + 20q^{73} - 36q^{81} - 48q^{85} - 24q^{93} - 40q^{97} + O(q^{100}) \)

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.bj.a \(2\) \(2.683\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(-3\) \(0\) \(-5\) \(q+(-2+\zeta_{6})q^{3}+(-3+\zeta_{6})q^{7}+(3+\cdots)q^{9}+\cdots\)
336.2.bj.b \(2\) \(2.683\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(-3\) \(0\) \(-1\) \(q+(-2+\zeta_{6})q^{3}+(1-3\zeta_{6})q^{7}+(3-3\zeta_{6})q^{9}+\cdots\)
336.2.bj.c \(2\) \(2.683\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(3\) \(0\) \(1\) \(q+(2-\zeta_{6})q^{3}+(-1+3\zeta_{6})q^{7}+(3-3\zeta_{6})q^{9}+\cdots\)
336.2.bj.d \(2\) \(2.683\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(3\) \(0\) \(5\) \(q+(2-\zeta_{6})q^{3}+(3-\zeta_{6})q^{7}+(3-3\zeta_{6})q^{9}+\cdots\)
336.2.bj.e \(8\) \(2.683\) 8.0.8275904784.2 None \(0\) \(-3\) \(0\) \(-6\) \(q+(1-\beta _{1}-\beta _{5}+\beta _{6})q^{3}+(1-\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
336.2.bj.f \(8\) \(2.683\) 8.0.303595776.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(1-2\beta _{2}+\beta _{4}+2\beta _{6})q^{5}+\cdots\)
336.2.bj.g \(8\) \(2.683\) 8.0.8275904784.2 None \(0\) \(3\) \(0\) \(6\) \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{4}-\beta _{7})q^{5}+(3+\cdots)q^{7}+\cdots\)

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

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