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

• Label: 1078.2.i
• Level: $1078$
• Weight: $2$
• Character orbit: 1078.i
• Rep. character: $\chi_{1078}(901,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $80$
• Newform subspaces: $4$
• Sturm bound: $336$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.i (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
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	368	80	288
Cusp forms	304	80	224
Eisenstein series	64	0	64

Trace form

80 * q + 40 * q^4 + 12 * q^5 + 24 * q^9 - 12 * q^11 + 24 * q^15 - 40 * q^16 + 16 * q^22 - 16 * q^23 + 56 * q^25 + 36 * q^26 + 12 * q^31 + 24 * q^33 + 48 * q^36 + 24 * q^37 - 12 * q^38 + 12 * q^44 + 108 * q^45 - 24 * q^47 + 28 * q^53 + 12 * q^58 - 60 * q^59 + 12 * q^60 - 80 * q^64 - 48 * q^66 - 28 * q^67 - 24 * q^71 - 60 * q^75 - 12 * q^80 - 16 * q^81 - 28 * q^86 + 8 * q^88 - 96 * q^89 - 32 * q^92 + 76 * q^93 - 144 * 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.i.a	$1078$	$2$	1078.i	77.i	$6$	$16$	$8$	$8.608$	\(\Q(\zeta_{48})\)	None		✓			1078.2.c.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta_1 q^{2}+(-\beta_{10}+\beta_{7}-\beta_{2})q^{3}+\cdots\)
1078.2.i.b	$1078$	$2$	1078.i	77.i	$6$	$16$	$8$	$8.608$	16.0.\(\cdots\).1	None					154.2.c.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{2}-\beta _{3})q^{2}+(-\beta _{4}+\beta _{9})q^{3}+\beta _{1}q^{4}+\cdots\)
1078.2.i.c	$1078$	$2$	1078.i	77.i	$6$	$16$	$8$	$8.608$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					154.2.i.a	$4$	$0$	\(0\)	\(0\)	\(12\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(\beta _{3}-\beta _{4}-\beta _{13})q^{3}+\beta _{10}q^{4}+\cdots\)
1078.2.i.d	$1078$	$2$	1078.i	77.i	$6$	$32$	$16$	$8.608$		None		✓	✓		1078.2.c.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

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