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

• Label: 1078.2.c
• Level: $1078$
• Weight: $2$
• Character orbit: 1078.c
• Rep. character: $\chi_{1078}(1077,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $3$
• Sturm bound: $336$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(336\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	184	40	144
Cusp forms	152	40	112
Eisenstein series	32	0	32

Trace form

40 * q - 40 * q^4 - 24 * q^9 + 24 * q^15 + 40 * q^16 + 8 * q^22 - 32 * q^23 - 56 * q^25 + 24 * q^36 + 56 * q^53 + 24 * q^58 - 24 * q^60 - 40 * q^64 + 40 * q^67 - 24 * q^71 - 48 * q^78 - 56 * q^81 - 8 * q^86 - 8 * q^88 + 32 * q^92 - 40 * q^93 + 48 * q^99

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.c.a	$1078$	$2$	1078.c	77.b	$2$	$8$	$8$	$8.608$	\(\Q(\zeta_{16})\)	None		✓			1078.2.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_1 q^{2}+(-\beta_{4}-\beta_{2})q^{3}-q^{4}+\cdots\)
1078.2.c.b	$1078$	$2$	1078.c	77.b	$2$	$16$	$16$	$8.608$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					154.2.i.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{9}q^{2}+\beta _{14}q^{3}-q^{4}+(-\beta _{8}+\beta _{11}+\cdots)q^{5}+\cdots\)
1078.2.c.c	$1078$	$2$	1078.c	77.b	$2$	$16$	$16$	$8.608$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			1078.2.c.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}-\beta _{5}q^{3}-q^{4}+(-\beta _{9}+\beta _{11}+\cdots)q^{5}+\cdots\)

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

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