Space of modular forms of level 59, weight 19, and Character 59.b

• Label: 59.19.b
• Level: $59$
• Weight: $19$
• Character orbit: 59.b
• Rep. character: $\chi_{59}(58,\cdot)$
• Character field: $\Q$
• Dimension: $89$
• Newform subspaces: $3$
• Sturm bound: $95$
• Trace bound: $1$

Defining parameters

Level:	$N$	$=$	$59$
Weight:	$k$	$=$	$19$
Character orbit:	$[\chi]$	$=$	59.b (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$59$
Character field:			$\Q$
Newform subspaces:			$3$
Sturm bound:			$95$
Trace bound:			$1$
Distinguishing $T_p$:			$2$, $3$

Dimensions

The following table gives the dimensions of various subspaces of $M_{19}(59, [\chi])$.

	Total	New	Old
Modular forms	91	91	0
Cusp forms	89	89	0
Eisenstein series	2	2	0

Trace form

89 * q - 47870 * q^3 - 11534338 * q^4 - 1461458 * q^5 + 42126406 * q^7 + 10679224559 * q^9 + 13944005596 * q^12 + 195444804060 * q^15 + 1494700729406 * q^16 - 320505008518 * q^17 - 20505417086 * q^19 - 921869660176 * q^20 + 455084712100 * q^21 - 2523101113242 * q^22 + 71373516329967 * q^25 + 4038771265458 * q^26 + 8087608595500 * q^27 + 45682997799418 * q^28 + 13384437130414 * q^29 + 320814281420436 * q^35 - 931742977189938 * q^36 - 1451467766454814 * q^41 - 2110695612420806 * q^45 - 2417237508941748 * q^46 - 1270141731516908 * q^48 + 21844186617126723 * q^49 - 5037084889546004 * q^51 - 251121963530482 * q^53 - 9487072418333676 * q^57 + 36718829609840937 * q^59 - 90187764941042672 * q^60 + 6330618081020380 * q^62 + 12833294777329138 * q^63 - 104394189854096326 * q^64 - 131353435035156400 * q^66 + 87497252943416734 * q^68 + 64801930768366326 * q^71 + 80283634292536118 * q^74 - 331206172164568922 * q^75 - 475525478749367576 * q^76 + 524338818805263656 * q^78 - 247822794733902050 * q^79 + 757098311310332504 * q^80 + 1437950587947411333 * q^81 + 1481351209847938312 * q^84 + 433641754218225164 * q^85 + 1059229941373163878 * q^86 + 2102112542985519988 * q^87 + 1283382060222557034 * q^88 - 2893703721678163368 * q^94 + 1556843544295866892 * q^95

Decomposition of $S_{19}^{\mathrm{new}}(59, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
59.19.b.a	$59$	$19$	59.b	59.b	$2$	$1$	$1$	$121.178$	$\Q$	$\Q(\sqrt{-59})$	✓	✓			59.19.b.a	$2$	$0$	$0$	$10810$	$-1985254$	$-50982910$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+10810q^{3}+2^{18}q^{4}-1985254q^{5}+\cdots$
59.19.b.b	$59$	$19$	59.b	59.b	$2$	$2$	$2$	$121.178$	$\Q(\sqrt{177})$	$\Q(\sqrt{-59})$	✓	✓			59.19.b.b	$2$	$0$	$0$	$-10810$	$1985254$	$50982910$	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q+(-5405-616\beta )q^{3}+2^{18}q^{4}+(992627+\cdots)q^{5}+\cdots$
59.19.b.c	$59$	$19$	59.b	59.b	$2$	$86$	$86$	$121.178$		None		✓	✓		59.19.b.c	$2$	$0$	$0$	$-47870$	$-1461458$	$42126406$		$\mathrm{SU}(2)[C_{2}]$