Properties

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

Related objects

Downloads

Learn more

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: \(\Q(\zeta_{6})\)
Newform subspaces: \( 6 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(336, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
336.2.bc.a 336.bc 21.g $2$ $2.683$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(-3\) \(0\) \(5\) $\mathrm{U}(1)[D_{6}]$ \(q+(-1-\zeta_{6})q^{3}+(2+\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots\)
336.2.bc.b 336.bc 21.g $2$ $2.683$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(-4\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+2\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(-1-2\zeta_{6})q^{7}+\cdots\)
336.2.bc.c 336.bc 21.g $2$ $2.683$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(3\) \(0\) \(-1\) $\mathrm{U}(1)[D_{6}]$ \(q+(1+\zeta_{6})q^{3}+(-2+3\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots\)
336.2.bc.d 336.bc 21.g $2$ $2.683$ \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(3\) \(-4\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2-\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(-1-2\zeta_{6})q^{7}+\cdots\)
336.2.bc.e 336.bc 21.g $4$ $2.683$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(10\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{12}^{2}q^{3}+(-\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+\cdots\)
336.2.bc.f 336.bc 21.g $16$ $2.683$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{5}+\beta _{8})q^{3}-\beta _{14}q^{5}+\beta _{10}q^{7}+\cdots\)

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

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