Properties

Label 336.2.q
Level 336
Weight 2
Character orbit q
Rep. character \(\chi_{336}(193,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 16
Newforms 7
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.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newforms: \( 7 \)
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

\( 16q - 2q^{3} - 2q^{7} - 8q^{9} + O(q^{10}) \) \( 16q - 2q^{3} - 2q^{7} - 8q^{9} + 4q^{11} - 10q^{19} + 16q^{23} - 12q^{25} + 4q^{27} + 16q^{29} + 14q^{31} - 4q^{33} + 36q^{35} - 8q^{37} + 2q^{39} + 16q^{41} - 12q^{43} - 12q^{47} - 16q^{49} - 16q^{53} - 56q^{55} - 8q^{57} - 16q^{59} - 8q^{61} - 2q^{63} - 8q^{65} - 6q^{67} + 24q^{71} + 12q^{73} - 14q^{75} + 8q^{77} + 18q^{79} - 8q^{81} - 24q^{83} - 16q^{85} + 12q^{87} + 16q^{89} + 54q^{91} + 8q^{93} - 36q^{95} + 8q^{97} - 8q^{99} + O(q^{100}) \)

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.q.a \(2\) \(2.683\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-2\) \(-5\) \(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots\)
336.2.q.b \(2\) \(2.683\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-1\) \(-1\) \(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
336.2.q.c \(2\) \(2.683\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(2\) \(-1\) \(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}+(-2+3\zeta_{6})q^{7}+\cdots\)
336.2.q.d \(2\) \(2.683\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-3\) \(-5\) \(q+(1-\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+\cdots\)
336.2.q.e \(2\) \(2.683\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(1\) \(-1\) \(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
336.2.q.f \(2\) \(2.683\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(2\) \(5\) \(q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
336.2.q.g \(4\) \(2.683\) \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(0\) \(-2\) \(1\) \(6\) \(q+(-1+\beta _{2})q^{3}+(-1+2\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(336, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)