Properties

Label 336.2.bl
Level 336
Weight 2
Character orbit bl
Rep. character \(\chi_{336}(31,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 16
Newforms 8
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.bl (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 28 \)
Character field: \(\Q(\zeta_{6})\)
Newforms: \( 8 \)
Sturm bound: \(128\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

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

Total New Old
Modular forms 152 16 136
Cusp forms 104 16 88
Eisenstein series 48 0 48

Trace form

\( 16q - 8q^{9} + O(q^{10}) \) \( 16q - 8q^{9} + 8q^{21} + 20q^{25} + 36q^{33} + 4q^{37} - 56q^{49} - 24q^{53} - 8q^{57} - 72q^{61} - 24q^{65} + 12q^{73} - 8q^{81} + 96q^{85} - 28q^{93} + O(q^{100}) \)

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.bl.a \(2\) \(2.683\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-6\) \(1\) \(q+(-1+\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+(2+\cdots)q^{7}+\cdots\)
336.2.bl.b \(2\) \(2.683\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-3\) \(-5\) \(q+(-1+\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(-3+\cdots)q^{7}+\cdots\)
336.2.bl.c \(2\) \(2.683\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(3\) \(1\) \(q+(-1+\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}+(-1+\cdots)q^{7}+\cdots\)
336.2.bl.d \(2\) \(2.683\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(6\) \(1\) \(q+(-1+\zeta_{6})q^{3}+(4-2\zeta_{6})q^{5}+(2-3\zeta_{6})q^{7}+\cdots\)
336.2.bl.e \(2\) \(2.683\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-6\) \(-1\) \(q+(1-\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots\)
336.2.bl.f \(2\) \(2.683\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-3\) \(5\) \(q+(1-\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(3-\zeta_{6})q^{7}+\cdots\)
336.2.bl.g \(2\) \(2.683\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(3\) \(-1\) \(q+(1-\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
336.2.bl.h \(2\) \(2.683\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(6\) \(-1\) \(q+(1-\zeta_{6})q^{3}+(4-2\zeta_{6})q^{5}+(-2+3\zeta_{6})q^{7}+\cdots\)

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

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