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Properties

Label 336.3.be
Level $336$
Weight $3$
Character orbit 336.be
Rep. character $\chi_{336}(79,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
Newform subspaces $6$
Sturm bound $192$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 336.be (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 6 \)
Sturm bound: \(192\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(336, [\chi])\).

Total New Old
Modular forms 280 32 248
Cusp forms 232 32 200
Eisenstein series 48 0 48

Trace form

\( 32 q + 48 q^{9} + O(q^{10}) \) \( 32 q + 48 q^{9} - 16 q^{13} - 48 q^{21} - 104 q^{25} + 72 q^{33} + 40 q^{37} + 96 q^{41} + 416 q^{49} + 48 q^{53} - 48 q^{57} - 32 q^{61} - 240 q^{65} - 376 q^{73} - 288 q^{77} - 144 q^{81} + 384 q^{85} - 672 q^{89} + 216 q^{93} + 272 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(336, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
336.3.be.a 336.be 28.g $4$ $9.155$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(0\) \(-6\) \(1\) \(12\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\beta _{2})q^{3}+(-1+2\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
336.3.be.b 336.be 28.g $4$ $9.155$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(0\) \(6\) \(1\) \(-12\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\beta _{2})q^{3}+(-1+2\beta _{1}+\beta _{2}-\beta _{3})q^{5}+\cdots\)
336.3.be.c 336.be 28.g $6$ $9.155$ 6.0.2682209403.3 None \(0\) \(-9\) \(-2\) \(11\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\beta _{1})q^{3}+(-\beta _{1}+\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots\)
336.3.be.d 336.be 28.g $6$ $9.155$ 6.0.1364138928.1 None \(0\) \(-9\) \(1\) \(-11\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-2+\beta _{1})q^{3}+\beta _{4}q^{5}+(-2+\beta _{2}+\cdots)q^{7}+\cdots\)
336.3.be.e 336.be 28.g $6$ $9.155$ 6.0.2682209403.3 None \(0\) \(9\) \(-2\) \(-11\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\beta _{1})q^{3}+(-\beta _{1}+\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
336.3.be.f 336.be 28.g $6$ $9.155$ 6.0.1364138928.1 None \(0\) \(9\) \(1\) \(11\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2-\beta _{1})q^{3}+\beta _{4}q^{5}+(3-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(336, [\chi])\) into lower level spaces

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