Space of modular forms of level 1078, weight 2, and Character 1078.e

• Label: 1078.2.e
• Level: $1078$
• Weight: $2$
• Character orbit: 1078.e
• Rep. character: $\chi_{1078}(67,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $64$
• Newform subspaces: $22$
• Sturm bound: $336$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 22 \)
Sturm bound:			\(336\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(3\), \(5\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1078, [\chi])\).

	Total	New	Old
Modular forms	368	64	304
Cusp forms	304	64	240
Eisenstein series	64	0	64

Trace form

64 * q - 32 * q^4 - 4 * q^5 - 8 * q^6 - 24 * q^9 - 8 * q^13 + 8 * q^15 - 32 * q^16 + 12 * q^17 - 16 * q^18 + 8 * q^20 - 32 * q^23 + 4 * q^24 - 40 * q^25 - 12 * q^26 + 24 * q^27 + 8 * q^29 - 4 * q^31 - 4 * q^33 + 8 * q^34 + 48 * q^36 + 48 * q^37 - 4 * q^38 + 44 * q^39 + 24 * q^41 - 40 * q^43 + 4 * q^45 - 4 * q^46 + 16 * q^47 - 32 * q^50 - 36 * q^51 + 4 * q^52 - 20 * q^53 + 16 * q^54 - 8 * q^57 + 12 * q^58 - 4 * q^59 - 4 * q^60 + 36 * q^61 - 24 * q^62 + 64 * q^64 + 20 * q^65 - 8 * q^66 + 52 * q^67 + 12 * q^68 - 24 * q^69 + 56 * q^71 - 16 * q^72 - 16 * q^73 + 20 * q^74 - 60 * q^75 + 64 * q^78 + 20 * q^79 - 4 * q^80 - 64 * q^81 - 8 * q^82 - 40 * q^83 - 144 * q^85 - 20 * q^86 + 12 * q^87 - 72 * q^90 + 64 * q^92 + 44 * q^93 - 8 * q^94 - 36 * q^95 + 4 * q^96 + 96 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(1078, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1078.2.e.a	$1078$	$2$	1078.e	7.c	$3$	$2$	$1$	$8.608$	\(\Q(\sqrt{-3}) \)	None		✓			1078.2.a.h	$2$	$0$	\(-1\)	\(-2\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.b	$1078$	$2$	1078.e	7.c	$3$	$2$	$1$	$8.608$	\(\Q(\sqrt{-3}) \)	None					154.2.a.c	$2$	$0$	\(-1\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-2\zeta_{6}q^{5}+\cdots\)
1078.2.e.c	$1078$	$2$	1078.e	7.c	$3$	$2$	$1$	$8.608$	\(\Q(\sqrt{-3}) \)	None					154.2.a.c	$2$	$0$	\(-1\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+2\zeta_{6}q^{5}+\cdots\)
1078.2.e.d	$1078$	$2$	1078.e	7.c	$3$	$2$	$1$	$8.608$	\(\Q(\sqrt{-3}) \)	None					154.2.e.b	$2$	$0$	\(-1\)	\(1\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.e	$1078$	$2$	1078.e	7.c	$3$	$2$	$1$	$8.608$	\(\Q(\sqrt{-3}) \)	None		✓			1078.2.a.h	$2$	$0$	\(-1\)	\(2\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.f	$1078$	$2$	1078.e	7.c	$3$	$2$	$1$	$8.608$	\(\Q(\sqrt{-3}) \)	None					154.2.e.a	$2$	$0$	\(-1\)	\(3\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.g	$1078$	$2$	1078.e	7.c	$3$	$2$	$1$	$8.608$	\(\Q(\sqrt{-3}) \)	None					154.2.e.d	$2$	$0$	\(1\)	\(-3\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.h	$1078$	$2$	1078.e	7.c	$3$	$2$	$1$	$8.608$	\(\Q(\sqrt{-3}) \)	None					154.2.a.b	$2$	$0$	\(1\)	\(-2\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.i	$1078$	$2$	1078.e	7.c	$3$	$2$	$1$	$8.608$	\(\Q(\sqrt{-3}) \)	None					154.2.a.a	$2$	$0$	\(1\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-4\zeta_{6}q^{5}+\cdots\)
1078.2.e.j	$1078$	$2$	1078.e	7.c	$3$	$2$	$1$	$8.608$	\(\Q(\sqrt{-3}) \)	None					154.2.a.a	$2$	$0$	\(1\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+4\zeta_{6}q^{5}+\cdots\)
1078.2.e.k	$1078$	$2$	1078.e	7.c	$3$	$2$	$1$	$8.608$	\(\Q(\sqrt{-3}) \)	None					154.2.e.c	$2$	$0$	\(1\)	\(1\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.l	$1078$	$2$	1078.e	7.c	$3$	$2$	$1$	$8.608$	\(\Q(\sqrt{-3}) \)	None					154.2.a.b	$2$	$0$	\(1\)	\(2\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.m	$1078$	$2$	1078.e	7.c	$3$	$4$	$2$	$8.608$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None					154.2.e.e	$2$	$0$	\(-2\)	\(-2\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1078.2.e.n	$1078$	$2$	1078.e	7.c	$3$	$4$	$2$	$8.608$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None					154.2.a.d	$2$	$0$	\(-2\)	\(-2\)	\(2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(-1-\beta _{1}-\beta _{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1078.2.e.o	$1078$	$2$	1078.e	7.c	$3$	$4$	$2$	$8.608$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			1078.2.a.v	$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{2}+2\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+\cdots\)
1078.2.e.p	$1078$	$2$	1078.e	7.c	$3$	$4$	$2$	$8.608$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			1078.2.a.u	$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(-3\beta _{1}+\cdots)q^{5}+\cdots\)
1078.2.e.q	$1078$	$2$	1078.e	7.c	$3$	$4$	$2$	$8.608$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None					154.2.a.d	$2$	$0$	\(-2\)	\(2\)	\(-2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)
1078.2.e.r	$1078$	$2$	1078.e	7.c	$3$	$4$	$2$	$8.608$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			1078.2.a.r	$4$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(-1-\beta _{2})q^{4}-\beta _{3}q^{6}+\cdots\)
1078.2.e.s	$1078$	$2$	1078.e	7.c	$3$	$4$	$2$	$8.608$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			1078.2.a.q	$4$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
1078.2.e.t	$1078$	$2$	1078.e	7.c	$3$	$4$	$2$	$8.608$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			1078.2.a.p	$4$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}-2\beta _{1}q^{5}-q^{8}+\cdots\)
1078.2.e.u	$1078$	$2$	1078.e	7.c	$3$	$4$	$2$	$8.608$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			1078.2.a.o	$4$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}-\beta _{1}q^{5}-q^{8}+\cdots\)
1078.2.e.v	$1078$	$2$	1078.e	7.c	$3$	$4$	$2$	$8.608$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None					154.2.e.f	$2$	$0$	\(2\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1078, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1078, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(539, [\chi])\)\(^{\oplus 2}\)