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

• Label: 3840.2.k
• Level: $3840$
• Weight: $2$
• Character orbit: 3840.k
• Rep. character: $\chi_{3840}(1921,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $30$
• Sturm bound: $1536$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 3840 = 2^{8} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3840.k (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 30 \)
Sturm bound:			\(1536\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(17\), \(23\), \(31\), \(47\)

Dimensions

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

	Total	New	Old
Modular forms	816	64	752
Cusp forms	720	64	656
Eisenstein series	96	0	96

Trace form

\( 64 q - 64 q^{9} - 64 q^{25} + 128 q^{49} - 64 q^{57} - 64 q^{73} + 64 q^{81} + 64 q^{97}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3840.2.k.a	$3840$	$2$	3840.k	8.b	$2$	$2$	$2$	$30.663$	\(\Q(\sqrt{-1}) \)	None					120.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}-i q^{5}-4 q^{7}-q^{9}+6 i q^{13}+\cdots\)
3840.2.k.b	$3840$	$2$	3840.k	8.b	$2$	$2$	$2$	$30.663$	\(\Q(\sqrt{-1}) \)	None					1920.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+i q^{5}-4 q^{7}-q^{9}+2 i q^{11}+\cdots\)
3840.2.k.c	$3840$	$2$	3840.k	8.b	$2$	$2$	$2$	$30.663$	\(\Q(\sqrt{-1}) \)	None					480.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}-i q^{5}-4 q^{7}-q^{9}-4 i q^{11}+\cdots\)
3840.2.k.d	$3840$	$2$	3840.k	8.b	$2$	$2$	$2$	$30.663$	\(\Q(\sqrt{-1}) \)	None					480.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+i q^{5}-4 q^{7}-q^{9}+2 i q^{13}+\cdots\)
3840.2.k.e	$3840$	$2$	3840.k	8.b	$2$	$2$	$2$	$30.663$	\(\Q(\sqrt{-1}) \)	None					1920.2.a.f	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}-i q^{5}-4 q^{7}-q^{9}+6 i q^{11}+\cdots\)
3840.2.k.f	$3840$	$2$	3840.k	8.b	$2$	$2$	$2$	$30.663$	\(\Q(\sqrt{-1}) \)	None					30.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}-i q^{5}-4 q^{7}-q^{9}-2 i q^{13}+\cdots\)
3840.2.k.g	$3840$	$2$	3840.k	8.b	$2$	$2$	$2$	$30.663$	\(\Q(\sqrt{-1}) \)	None					1920.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}-i q^{5}-2 q^{7}-q^{9}-2 i q^{11}+\cdots\)
3840.2.k.h	$3840$	$2$	3840.k	8.b	$2$	$2$	$2$	$30.663$	\(\Q(\sqrt{-1}) \)	None					1920.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+i q^{5}-2 q^{7}-q^{9}-6 i q^{11}+\cdots\)
3840.2.k.i	$3840$	$2$	3840.k	8.b	$2$	$2$	$2$	$30.663$	\(\Q(\sqrt{-1}) \)	None					1920.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}-i q^{5}-2 q^{7}-q^{9}-2 i q^{11}+\cdots\)
3840.2.k.j	$3840$	$2$	3840.k	8.b	$2$	$2$	$2$	$30.663$	\(\Q(\sqrt{-1}) \)	None					120.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}-i q^{5}-q^{9}-4 i q^{11}+6 i q^{13}+\cdots\)
3840.2.k.k	$3840$	$2$	3840.k	8.b	$2$	$2$	$2$	$30.663$	\(\Q(\sqrt{-1}) \)	None					480.2.a.b	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+i q^{5}-q^{9}-4 i q^{11}+2 i q^{13}+\cdots\)
3840.2.k.l	$3840$	$2$	3840.k	8.b	$2$	$2$	$2$	$30.663$	\(\Q(\sqrt{-1}) \)	None					1920.2.a.d	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}-i q^{5}-q^{9}-2 i q^{11}+4 i q^{13}+\cdots\)
3840.2.k.m	$3840$	$2$	3840.k	8.b	$2$	$2$	$2$	$30.663$	\(\Q(\sqrt{-1}) \)	None					15.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}-i q^{5}-q^{9}+4 i q^{11}-2 i q^{13}+\cdots\)
3840.2.k.n	$3840$	$2$	3840.k	8.b	$2$	$2$	$2$	$30.663$	\(\Q(\sqrt{-1}) \)	None					480.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}-i q^{5}-q^{9}+2 i q^{13}-q^{15}+\cdots\)
3840.2.k.o	$3840$	$2$	3840.k	8.b	$2$	$2$	$2$	$30.663$	\(\Q(\sqrt{-1}) \)	None					120.2.a.b	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}-i q^{5}-q^{9}+4 i q^{11}+6 i q^{13}+\cdots\)
3840.2.k.p	$3840$	$2$	3840.k	8.b	$2$	$2$	$2$	$30.663$	\(\Q(\sqrt{-1}) \)	None					480.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+i q^{5}-q^{9}+4 i q^{11}+2 i q^{13}+\cdots\)
3840.2.k.q	$3840$	$2$	3840.k	8.b	$2$	$2$	$2$	$30.663$	\(\Q(\sqrt{-1}) \)	None					1920.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}-i q^{5}-q^{9}+2 i q^{11}+4 i q^{13}+\cdots\)
3840.2.k.r	$3840$	$2$	3840.k	8.b	$2$	$2$	$2$	$30.663$	\(\Q(\sqrt{-1}) \)	None					15.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}-i q^{5}-q^{9}-4 i q^{11}-2 i q^{13}+\cdots\)
3840.2.k.s	$3840$	$2$	3840.k	8.b	$2$	$2$	$2$	$30.663$	\(\Q(\sqrt{-1}) \)	None					480.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+i q^{5}-q^{9}-2 i q^{13}+q^{15}+\cdots\)
3840.2.k.t	$3840$	$2$	3840.k	8.b	$2$	$2$	$2$	$30.663$	\(\Q(\sqrt{-1}) \)	None					1920.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}-i q^{5}+2 q^{7}-q^{9}+2 i q^{11}+\cdots\)
3840.2.k.u	$3840$	$2$	3840.k	8.b	$2$	$2$	$2$	$30.663$	\(\Q(\sqrt{-1}) \)	None					1920.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}-i q^{5}+2 q^{7}-q^{9}+2 i q^{11}+\cdots\)
3840.2.k.v	$3840$	$2$	3840.k	8.b	$2$	$2$	$2$	$30.663$	\(\Q(\sqrt{-1}) \)	None					1920.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}-i q^{5}+2 q^{7}-q^{9}-6 i q^{11}+\cdots\)
3840.2.k.w	$3840$	$2$	3840.k	8.b	$2$	$2$	$2$	$30.663$	\(\Q(\sqrt{-1}) \)	None					480.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+i q^{5}+4 q^{7}-q^{9}+2 i q^{13}+\cdots\)
3840.2.k.x	$3840$	$2$	3840.k	8.b	$2$	$2$	$2$	$30.663$	\(\Q(\sqrt{-1}) \)	None					1920.2.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+i q^{5}+4 q^{7}-q^{9}+6 i q^{11}+\cdots\)
3840.2.k.y	$3840$	$2$	3840.k	8.b	$2$	$2$	$2$	$30.663$	\(\Q(\sqrt{-1}) \)	None					30.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}-i q^{5}+4 q^{7}-q^{9}-2 i q^{13}+\cdots\)
3840.2.k.z	$3840$	$2$	3840.k	8.b	$2$	$2$	$2$	$30.663$	\(\Q(\sqrt{-1}) \)	None					120.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+i q^{5}+4 q^{7}-q^{9}-6 i q^{13}+\cdots\)
3840.2.k.ba	$3840$	$2$	3840.k	8.b	$2$	$2$	$2$	$30.663$	\(\Q(\sqrt{-1}) \)	None					1920.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+i q^{5}+4 q^{7}-q^{9}-2 i q^{11}+\cdots\)
3840.2.k.bb	$3840$	$2$	3840.k	8.b	$2$	$2$	$2$	$30.663$	\(\Q(\sqrt{-1}) \)	None					480.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+i q^{5}+4 q^{7}-q^{9}-4 i q^{11}+\cdots\)
3840.2.k.bc	$3840$	$2$	3840.k	8.b	$2$	$4$	$4$	$30.663$	\(\Q(i, \sqrt{17})\)	None					1920.2.a.y	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+\beta _{1}q^{5}+(-1+\beta _{3})q^{7}-q^{9}+\cdots\)
3840.2.k.bd	$3840$	$2$	3840.k	8.b	$2$	$4$	$4$	$30.663$	\(\Q(i, \sqrt{17})\)	None					1920.2.a.y	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}-\beta _{1}q^{5}+(1-\beta _{3})q^{7}-q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(3840, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1280, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1920, [\chi])\)\(^{\oplus 2}\)