Space of modular forms of level 3840, weight 2, and Character 3840.f

• Label: 3840.2.f
• Level: $3840$
• Weight: $2$
• Character orbit: 3840.f
• Rep. character: $\chi_{3840}(769,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $14$
• Sturm bound: $1536$
• Trace bound: $31$

Defining parameters

Level:	\( N \)	\(=\)	\( 3840 = 2^{8} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3840.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 14 \)
Sturm bound:			\(1536\)
Trace bound:			\(31\)
Distinguishing \(T_p\):			\(7\), \(11\), \(29\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3840, [\chi])\).

	Total	New	Old
Modular forms	816	96	720
Cusp forms	720	96	624
Eisenstein series	96	0	96

Trace form

\( 96 q - 96 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3840, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3840.2.f.a	$3840$	$2$	3840.f	5.b	$2$	$2$	$2$	$30.663$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+(-2-i)q^{5}+2iq^{7}-q^{9}+\cdots\)
3840.2.f.b	$3840$	$2$	3840.f	5.b	$2$	$2$	$2$	$30.663$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+(-2+i)q^{5}+2iq^{7}-q^{9}+\cdots\)
3840.2.f.c	$3840$	$2$	3840.f	5.b	$2$	$2$	$2$	$30.663$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+(2-i)q^{5}+2iq^{7}-q^{9}-2q^{11}+\cdots\)
3840.2.f.d	$3840$	$2$	3840.f	5.b	$2$	$2$	$2$	$30.663$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+(2+i)q^{5}+2iq^{7}-q^{9}+2q^{11}+\cdots\)
3840.2.f.e	$3840$	$2$	3840.f	5.b	$2$	$6$	$6$	$30.663$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{4}q^{5}+(2\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
3840.2.f.f	$3840$	$2$	3840.f	5.b	$2$	$6$	$6$	$30.663$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}-\beta _{4}q^{5}+(2\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
3840.2.f.g	$3840$	$2$	3840.f	5.b	$2$	$6$	$6$	$30.663$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}-\beta _{3}q^{5}+(2\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
3840.2.f.h	$3840$	$2$	3840.f	5.b	$2$	$6$	$6$	$30.663$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{3}q^{5}+(2\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
3840.2.f.i	$3840$	$2$	3840.f	5.b	$2$	$8$	$8$	$30.663$	8.0.49787136.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{5}q^{5}+(\beta _{3}-\beta _{7})q^{7}-q^{9}+\cdots\)
3840.2.f.j	$3840$	$2$	3840.f	5.b	$2$	$8$	$8$	$30.663$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{24}q^{3}-\zeta_{24}^{3}q^{5}-q^{9}+(\zeta_{24}^{3}+\cdots)q^{13}+\cdots\)
3840.2.f.k	$3840$	$2$	3840.f	5.b	$2$	$8$	$8$	$30.663$	8.0.49787136.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}-\beta _{5}q^{5}+(\beta _{3}-\beta _{7})q^{7}-q^{9}+\cdots\)
3840.2.f.l	$3840$	$2$	3840.f	5.b	$2$	$12$	$12$	$30.663$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+\beta _{6}q^{5}-\beta _{1}q^{7}-q^{9}+(-\beta _{8}+\cdots)q^{11}+\cdots\)
3840.2.f.m	$3840$	$2$	3840.f	5.b	$2$	$12$	$12$	$30.663$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}-\beta _{2}q^{5}-\beta _{1}q^{7}-q^{9}+(-\beta _{8}+\cdots)q^{11}+\cdots\)
3840.2.f.n	$3840$	$2$	3840.f	5.b	$2$	$16$	$16$	$30.663$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{23}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{3}-\beta _{3}q^{5}-\beta _{13}q^{7}-q^{9}-\beta _{1}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3840, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3840, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1280, [\chi])\)\(^{\oplus 2}\)