Space of modular forms of level 3456, weight 2, and Character 3456.f

• Label: 3456.2.f
• Level: $3456$
• Weight: $2$
• Character orbit: 3456.f
• Rep. character: $\chi_{3456}(1727,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $9$
• Sturm bound: $1152$
• Trace bound: $25$

Defining parameters

Level:	\( N \)	\(=\)	\( 3456 = 2^{7} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3456.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(1152\)
Trace bound:			\(25\)
Distinguishing \(T_p\):			\(5\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3456, [\chi])\).

	Total	New	Old
Modular forms	624	64	560
Cusp forms	528	64	464
Eisenstein series	96	0	96

Trace form

\( 64 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3456, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3456.2.f.a	$3456$	$2$	3456.f	24.f	$2$	$4$	$4$	$27.596$	\(\Q(\sqrt{2}, \sqrt{-3})\)	\(\Q(\sqrt{-6}) \)		$4$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+(-3-\beta _{1})q^{5}+(\beta _{2}-\beta _{3})q^{7}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
3456.2.f.b	$3456$	$2$	3456.f	24.f	$2$	$4$	$4$	$27.596$	\(\Q(\sqrt{2}, \sqrt{-3})\)	\(\Q(\sqrt{-6}) \)		$4$	$0$	\(0\)	\(0\)	\(12\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+(3-\beta _{1})q^{5}+(\beta _{2}+\beta _{3})q^{7}+(\beta _{2}+2\beta _{3})q^{11}+\cdots\)
3456.2.f.c	$3456$	$2$	3456.f	24.f	$2$	$8$	$8$	$27.596$	8.0.56070144.2	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}-\beta _{7}q^{7}+(\beta _{2}-\beta _{3})q^{11}+(-\beta _{2}+\cdots)q^{13}+\cdots\)
3456.2.f.d	$3456$	$2$	3456.f	24.f	$2$	$8$	$8$	$27.596$	8.0.12960000.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{3})q^{5}+\beta _{6}q^{7}+(\beta _{4}-\beta _{5})q^{11}+\cdots\)
3456.2.f.e	$3456$	$2$	3456.f	24.f	$2$	$8$	$8$	$27.596$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{24}^{3}q^{5}+\zeta_{24}q^{7}+\zeta_{24}^{5}q^{11}+\cdots\)
3456.2.f.f	$3456$	$2$	3456.f	24.f	$2$	$8$	$8$	$27.596$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{24}^{3}q^{5}+\zeta_{24}^{6}q^{7}-\zeta_{24}q^{11}+\cdots\)
3456.2.f.g	$3456$	$2$	3456.f	24.f	$2$	$8$	$8$	$27.596$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{24}^{4}q^{5}+\zeta_{24}^{6}q^{7}-\zeta_{24}^{5}q^{11}+\cdots\)
3456.2.f.h	$3456$	$2$	3456.f	24.f	$2$	$8$	$8$	$27.596$	8.0.12960000.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{3})q^{5}+\beta _{6}q^{7}+(\beta _{4}-\beta _{5})q^{11}+\cdots\)
3456.2.f.i	$3456$	$2$	3456.f	24.f	$2$	$8$	$8$	$27.596$	8.0.56070144.2	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}-\beta _{7}q^{7}+(\beta _{2}-\beta _{3})q^{11}+(\beta _{2}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3456, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3456, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 15}\)