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

• Label: 578.2.f
• Level: $578$
• Weight: $2$
• Character orbit: 578.f
• Rep. character: $\chi_{578}(35,\cdot)$
• Character field: $\Q(\zeta_{17})$
• Dimension: $416$
• Newform subspaces: $2$
• Sturm bound: $153$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 578 = 2 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	578.f (of order \(17\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 289 \)
Character field:			\(\Q(\zeta_{17})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(153\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	1248	416	832
Cusp forms	1184	416	768
Eisenstein series	64	0	64

Trace form

416 * q - 2 * q^2 - 2 * q^3 - 26 * q^4 + 11 * q^5 - 2 * q^6 - 4 * q^7 - 2 * q^8 - 38 * q^9 - 6 * q^10 - 18 * q^11 - 2 * q^12 - 12 * q^13 - 4 * q^14 - 20 * q^15 - 26 * q^16 - 16 * q^17 - 10 * q^18 - 12 * q^19 - 6 * q^20 + 66 * q^21 - 18 * q^22 - 24 * q^23 - 2 * q^24 + 5 * q^25 - 12 * q^26 + 7 * q^27 - 4 * q^28 - 30 * q^29 - 24 * q^30 - 28 * q^31 - 2 * q^32 + 74 * q^33 - 16 * q^34 - 44 * q^35 - 38 * q^36 - 34 * q^37 + 158 * q^38 + 84 * q^39 - 6 * q^40 - 48 * q^41 - 36 * q^42 - 44 * q^43 + 16 * q^44 + 228 * q^45 + 44 * q^46 - 10 * q^47 - 2 * q^48 - 86 * q^49 - 22 * q^50 - 2 * q^51 + 39 * q^52 - 6 * q^53 + 58 * q^54 - 64 * q^55 - 4 * q^56 - 88 * q^57 - 30 * q^58 - 52 * q^59 - 20 * q^60 - 58 * q^61 + 74 * q^62 + 70 * q^63 - 26 * q^64 - 84 * q^65 - 32 * q^66 + 51 * q^67 - 16 * q^68 + 150 * q^69 - 44 * q^70 - 72 * q^71 + 7 * q^72 - 76 * q^73 - 34 * q^74 + 138 * q^75 - 12 * q^76 - 30 * q^77 - 52 * q^78 + 82 * q^79 - 6 * q^80 + 14 * q^81 - 48 * q^82 - 38 * q^83 - 36 * q^84 + 102 * q^85 - 48 * q^86 - 108 * q^87 + 16 * q^88 - 76 * q^89 - 78 * q^90 + 32 * q^91 + 10 * q^92 - 124 * q^93 + 92 * q^94 - 120 * q^95 - 2 * q^96 - 112 * q^97 + 146 * q^98 - 162 * q^99

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.f.a	$578$	$2$	578.f	289.f	$17$	$192$	$12$	$4.615$		None		✓			578.2.f.a	$2$	$0$	\(12\)	\(0\)	\(-17\)	\(0\)		$\mathrm{SU}(2)[C_{17}]$
578.2.f.b	$578$	$2$	578.f	289.f	$17$	$224$	$14$	$4.615$		None		✓	✓		578.2.f.b	$2$	$0$	\(-14\)	\(-2\)	\(28\)	\(-4\)		$\mathrm{SU}(2)[C_{17}]$

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

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