Space of modular forms of level 578, weight 2, and Character 578.b

• Label: 578.2.b
• Level: $578$
• Weight: $2$
• Character orbit: 578.b
• Rep. character: $\chi_{578}(577,\cdot)$
• Character field: $\Q$
• Dimension: $22$
• Newform subspaces: $6$
• Sturm bound: $153$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 578 = 2 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	578.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(153\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(578, [\chi])\).

	Total	New	Old
Modular forms	94	22	72
Cusp forms	58	22	36
Eisenstein series	36	0	36

Trace form

22 * q + 2 * q^2 + 22 * q^4 + 2 * q^8 - 14 * q^9 - 8 * q^13 - 12 * q^15 + 22 * q^16 - 14 * q^18 + 12 * q^19 - 4 * q^21 - 14 * q^25 + 8 * q^26 + 16 * q^30 + 2 * q^32 - 24 * q^33 - 4 * q^35 - 14 * q^36 - 12 * q^38 + 4 * q^42 + 16 * q^43 - 4 * q^47 - 34 * q^49 - 10 * q^50 - 8 * q^52 - 4 * q^53 + 8 * q^55 - 16 * q^59 - 12 * q^60 + 22 * q^64 + 20 * q^66 + 24 * q^69 + 4 * q^70 - 14 * q^72 + 12 * q^76 + 8 * q^77 + 10 * q^81 + 36 * q^83 - 4 * q^84 - 12 * q^86 - 4 * q^87 - 20 * q^89 + 12 * q^93 + 4 * q^94 + 6 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(578, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
578.2.b.a	$578$	$2$	578.b	17.b	$2$	$2$	$2$	$4.615$	\(\Q(\sqrt{-1}) \)	None					34.2.a.a	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-2\beta q^{7}+\cdots\)
578.2.b.b	$578$	$2$	578.b	17.b	$2$	$2$	$2$	$4.615$	\(\Q(\sqrt{-2}) \)	None					34.2.c.a	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+\beta q^{3}+q^{4}+2\beta q^{5}-\beta q^{6}+\cdots\)
578.2.b.c	$578$	$2$	578.b	17.b	$2$	$2$	$2$	$4.615$	\(\Q(\sqrt{-2}) \)	None					34.2.c.b	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+3q^{9}+\beta q^{10}+\cdots\)
578.2.b.d	$578$	$2$	578.b	17.b	$2$	$4$	$4$	$4.615$	4.0.2048.2	None					34.2.d.a	$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+2\beta _{1}q^{5}+\beta _{1}q^{6}+\cdots\)
578.2.b.e	$578$	$2$	578.b	17.b	$2$	$6$	$6$	$4.615$	6.0.419904.1	None		✓			578.2.a.g	$2$	$0$	\(-6\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+(\beta _{1}+\beta _{3}+\beta _{5})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
578.2.b.f	$578$	$2$	578.b	17.b	$2$	$6$	$6$	$4.615$	6.0.419904.1	None		✓			578.2.a.e	$2$	$0$	\(6\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+(\beta _{1}-\beta _{3}-\beta _{5})q^{3}+q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(578, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(578, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(289, [\chi])\)\(^{\oplus 2}\)