Properties

Label 336.2.bc
Level 336
Weight 2
Character orbit bc
Rep. character \(\chi_{336}(17,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 28
Newforms 6
Sturm bound 128
Trace bound 5

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Defining parameters

Level: \( N \) = \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 336.bc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newforms: \( 6 \)
Sturm bound: \(128\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(13\)

Dimensions

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

Total New Old
Modular forms 152 36 116
Cusp forms 104 28 76
Eisenstein series 48 8 40

Trace form

\( 28q + 3q^{3} + 2q^{7} - q^{9} + O(q^{10}) \) \( 28q + 3q^{3} + 2q^{7} - q^{9} - 2q^{15} + 12q^{19} - q^{21} - 12q^{25} + 48q^{31} - 3q^{33} - 2q^{37} + 10q^{39} - 20q^{43} - 15q^{45} - 4q^{49} - 27q^{51} - 26q^{57} - 6q^{61} - 7q^{63} + 16q^{67} - 18q^{73} - 66q^{75} - 28q^{79} + 3q^{81} + 28q^{85} - 60q^{87} - 54q^{91} + q^{93} + 34q^{99} + O(q^{100}) \)

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.bc.a \(2\) \(2.683\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(-3\) \(0\) \(5\) \(q+(-1-\zeta_{6})q^{3}+(2+\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots\)
336.2.bc.b \(2\) \(2.683\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(-4\) \(q+(-1+2\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(-1-2\zeta_{6})q^{7}+\cdots\)
336.2.bc.c \(2\) \(2.683\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(3\) \(0\) \(-1\) \(q+(1+\zeta_{6})q^{3}+(-2+3\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots\)
336.2.bc.d \(2\) \(2.683\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(3\) \(-4\) \(q+(2-\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(-1-2\zeta_{6})q^{7}+\cdots\)
336.2.bc.e \(4\) \(2.683\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(10\) \(q-\zeta_{12}^{2}q^{3}+(-\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+\cdots\)
336.2.bc.f \(16\) \(2.683\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-4\) \(q+(-\beta _{5}+\beta _{8})q^{3}-\beta _{14}q^{5}+\beta _{10}q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(336, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)