Space of modular forms of level 2816, weight 2, and Character 2816.c

• Label: 2816.2.c
• Level: $2816$
• Weight: $2$
• Character orbit: 2816.c
• Rep. character: $\chi_{2816}(1409,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $26$
• Sturm bound: $768$
• Trace bound: $15$

Defining parameters

Level:	\( N \)	\(=\)	\( 2816 = 2^{8} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2816.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 26 \)
Sturm bound:			\(768\)
Trace bound:			\(15\)
Distinguishing \(T_p\):			\(3\), \(5\), \(7\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2816, [\chi])\).

	Total	New	Old
Modular forms	408	80	328
Cusp forms	360	80	280
Eisenstein series	48	0	48

Trace form

\( 80 q - 80 q^{9} - 80 q^{25} + 16 q^{49} + 64 q^{57} - 32 q^{65} + 96 q^{73} + 80 q^{81} + 32 q^{89} - 64 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2816, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2816.2.c.a	$2816$	$2$	2816.c	8.b	$2$	$2$	$2$	$22.486$	\(\Q(\sqrt{-1}) \)	None					352.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}-i q^{5}-4 q^{7}+2 q^{9}-i q^{11}+\cdots\)
2816.2.c.b	$2816$	$2$	2816.c	8.b	$2$	$2$	$2$	$22.486$	\(\Q(\sqrt{-1}) \)	None					352.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}-3 i q^{5}-4 q^{7}+2 q^{9}-i q^{11}+\cdots\)
2816.2.c.c	$2816$	$2$	2816.c	8.b	$2$	$2$	$2$	$22.486$	\(\Q(\sqrt{-1}) \)	None					1408.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2 i q^{5}-4 q^{7}+3 q^{9}+i q^{11}+\cdots\)
2816.2.c.d	$2816$	$2$	2816.c	8.b	$2$	$2$	$2$	$22.486$	\(\Q(\sqrt{-1}) \)	None					88.2.a.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3 i q^{3}+3 i q^{5}-2 q^{7}-6 q^{9}+\cdots\)
2816.2.c.e	$2816$	$2$	2816.c	8.b	$2$	$2$	$2$	$22.486$	\(\Q(\sqrt{-1}) \)	None					44.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+3 i q^{5}-2 q^{7}+2 q^{9}+i q^{11}+\cdots\)
2816.2.c.f	$2816$	$2$	2816.c	8.b	$2$	$2$	$2$	$22.486$	\(\Q(\sqrt{-1}) \)	None					11.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}-i q^{5}-2 q^{7}+2 q^{9}+i q^{11}+\cdots\)
2816.2.c.g	$2816$	$2$	2816.c	8.b	$2$	$2$	$2$	$22.486$	\(\Q(\sqrt{-1}) \)	None					352.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3 i q^{3}+i q^{5}-6 q^{9}+i q^{11}+\cdots\)
2816.2.c.h	$2816$	$2$	2816.c	8.b	$2$	$2$	$2$	$22.486$	\(\Q(\sqrt{-1}) \)	None					352.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3 i q^{3}-i q^{5}-6 q^{9}+i q^{11}+\cdots\)
2816.2.c.i	$2816$	$2$	2816.c	8.b	$2$	$2$	$2$	$22.486$	\(\Q(\sqrt{-1}) \)	None					88.2.a.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3 i q^{3}-3 i q^{5}+2 q^{7}-6 q^{9}+\cdots\)
2816.2.c.j	$2816$	$2$	2816.c	8.b	$2$	$2$	$2$	$22.486$	\(\Q(\sqrt{-1}) \)	None					11.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+i q^{5}+2 q^{7}+2 q^{9}+i q^{11}+\cdots\)
2816.2.c.k	$2816$	$2$	2816.c	8.b	$2$	$2$	$2$	$22.486$	\(\Q(\sqrt{-1}) \)	None					44.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}-3 i q^{5}+2 q^{7}+2 q^{9}+i q^{11}+\cdots\)
2816.2.c.l	$2816$	$2$	2816.c	8.b	$2$	$2$	$2$	$22.486$	\(\Q(\sqrt{-1}) \)	None					352.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+3 i q^{5}+4 q^{7}+2 q^{9}-i q^{11}+\cdots\)
2816.2.c.m	$2816$	$2$	2816.c	8.b	$2$	$2$	$2$	$22.486$	\(\Q(\sqrt{-1}) \)	None					352.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+i q^{5}+4 q^{7}+2 q^{9}-i q^{11}+\cdots\)
2816.2.c.n	$2816$	$2$	2816.c	8.b	$2$	$2$	$2$	$22.486$	\(\Q(\sqrt{-1}) \)	None					1408.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2 i q^{5}+4 q^{7}+3 q^{9}-i q^{11}+\cdots\)
2816.2.c.o	$2816$	$2$	2816.c	8.b	$2$	$4$	$4$	$22.486$	\(\Q(\zeta_{8})\)	None					1408.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_{2}+\beta_1)q^{3}-\beta_1 q^{5}+(-\beta_{3}-2)q^{7}+\cdots\)
2816.2.c.p	$2816$	$2$	2816.c	8.b	$2$	$4$	$4$	$22.486$	\(\Q(i, \sqrt{17})\)	None					88.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-\beta _{1}-2\beta _{2})q^{5}+(-2+2\beta _{3})q^{7}+\cdots\)
2816.2.c.q	$2816$	$2$	2816.c	8.b	$2$	$4$	$4$	$22.486$	\(\Q(i, \sqrt{6})\)	None					1408.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{2})q^{3}+3\beta _{1}q^{5}-\beta _{3}q^{7}+(-4+\cdots)q^{9}+\cdots\)
2816.2.c.r	$2816$	$2$	2816.c	8.b	$2$	$4$	$4$	$22.486$	\(\Q(i, \sqrt{6})\)	None					1408.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{2})q^{3}-3\beta _{1}q^{5}+\beta _{3}q^{7}+(-4+\cdots)q^{9}+\cdots\)
2816.2.c.s	$2816$	$2$	2816.c	8.b	$2$	$4$	$4$	$22.486$	\(\Q(i, \sqrt{17})\)	None					352.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(\beta _{1}+2\beta _{2})q^{5}+(-2+\beta _{3})q^{9}+\cdots\)
2816.2.c.t	$2816$	$2$	2816.c	8.b	$2$	$4$	$4$	$22.486$	\(\Q(i, \sqrt{17})\)	None					352.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-\beta _{1}-2\beta _{2})q^{5}+(-2+\beta _{3})q^{9}+\cdots\)
2816.2.c.u	$2816$	$2$	2816.c	8.b	$2$	$4$	$4$	$22.486$	\(\Q(\zeta_{8})\)	None					1408.2.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_{2}+\beta_1)q^{3}+(2\beta_{2}+\beta_1)q^{5}+\cdots\)
2816.2.c.v	$2816$	$2$	2816.c	8.b	$2$	$4$	$4$	$22.486$	\(\Q(\zeta_{8})\)	None					1408.2.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_{2}+\beta_1)q^{3}+(-2\beta_{2}-\beta_1)q^{5}+\cdots\)
2816.2.c.w	$2816$	$2$	2816.c	8.b	$2$	$4$	$4$	$22.486$	\(\Q(i, \sqrt{17})\)	None					88.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(\beta _{1}+2\beta _{2})q^{5}+(2-2\beta _{3})q^{7}+\cdots\)
2816.2.c.x	$2816$	$2$	2816.c	8.b	$2$	$4$	$4$	$22.486$	\(\Q(\zeta_{8})\)	None					1408.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_{2}+\beta_1)q^{3}+\beta_1 q^{5}+(\beta_{3}+2)q^{7}+\cdots\)
2816.2.c.y	$2816$	$2$	2816.c	8.b	$2$	$6$	$6$	$22.486$	6.0.5161984.1	None					1408.2.a.q	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}+\beta _{4})q^{3}+(-\beta _{3}-\beta _{5})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
2816.2.c.z	$2816$	$2$	2816.c	8.b	$2$	$6$	$6$	$22.486$	6.0.5161984.1	None					1408.2.a.q	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}+\beta _{4})q^{3}+(\beta _{3}+\beta _{5})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2816, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2816, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(352, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(704, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1408, [\chi])\)\(^{\oplus 2}\)