Space of modular forms of level 336, weight 2, and Character 336.bc

• 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: $5$

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 - 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

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

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
336.2.bc.a	$336$	$2$	336.bc	21.g	$6$	$2$	$1$	$2.683$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)					84.2.k.c	$4$	$0$	\(0\)	\(-3\)	\(0\)	\(5\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-1-\zeta_{6})q^{3}+(2+\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots\)
336.2.bc.b	$336$	$2$	336.bc	21.g	$6$	$2$	$1$	$2.683$	\(\Q(\sqrt{-3}) \)	None					84.2.k.a	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+2\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(-1-2\zeta_{6})q^{7}+\cdots\)
336.2.bc.c	$336$	$2$	336.bc	21.g	$6$	$2$	$1$	$2.683$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)					21.2.g.a	$4$	$0$	\(0\)	\(3\)	\(0\)	\(-1\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(1+\zeta_{6})q^{3}+(-2+3\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots\)
336.2.bc.d	$336$	$2$	336.bc	21.g	$6$	$2$	$1$	$2.683$	\(\Q(\sqrt{-3}) \)	None					84.2.k.a	$2$	$0$	\(0\)	\(3\)	\(3\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2-\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(-1-2\zeta_{6})q^{7}+\cdots\)
336.2.bc.e	$336$	$2$	336.bc	21.g	$6$	$4$	$2$	$2.683$	\(\Q(\zeta_{12})\)	None					42.2.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(10\)	$3$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta_{2} q^{3}+(\beta_{3}-\beta_{2})q^{5}+(\beta_1+2)q^{7}+\cdots\)
336.2.bc.f	$336$	$2$	336.bc	21.g	$6$	$16$	$8$	$2.683$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None			✓		168.2.u.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{8}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{5}+\beta _{8})q^{3}-\beta _{14}q^{5}+\beta _{10}q^{7}+\cdots\)

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

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