Space of modular forms of level 2793, weight 2, and trivial character

• Label: 2793.2.a
• Level: $2793$
• Weight: $2$
• Character orbit: 2793.a
• Rep. character: $\chi_{2793}(1,\cdot)$
• Character field: $\Q$
• Dimension: $122$
• Newform subspaces: $40$
• Sturm bound: $746$
• Trace bound: $5$

Defining parameters

Level:	$N$	$=$	$2793 = 3 \cdot 7^{2} \cdot 19$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	2793.a (trivial)
Character field:			$\Q$
Newform subspaces:			$40$
Sturm bound:			$746$
Trace bound:			$5$
Distinguishing $T_p$:			$2$, $5$, $11$, $13$, $17$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(2793))$.

	Total	New	Old
Modular forms	388	122	266
Cusp forms	357	122	235
Eisenstein series	31	0	31

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

$3$	$7$	$19$	Fricke	Dim
$+$	$+$	$+$	$+$	$14$
$+$	$+$	$-$	$-$	$14$
$+$	$-$	$+$	$-$	$15$
$+$	$-$	$-$	$+$	$18$
$-$	$+$	$+$	$-$	$18$
$-$	$+$	$-$	$+$	$10$
$-$	$-$	$+$	$+$	$12$
$-$	$-$	$-$	$-$	$21$
Plus space			$+$	$54$
Minus space			$-$	$68$

Trace form

122 * q + 2 * q^2 + 124 * q^4 - 6 * q^5 + 2 * q^6 + 6 * q^8 + 122 * q^9 - 8 * q^10 + 6 * q^11 - 8 * q^12 - 12 * q^13 + 4 * q^15 + 136 * q^16 - 18 * q^17 + 2 * q^18 + 4 * q^19 + 4 * q^20 + 16 * q^22 + 12 * q^23 + 18 * q^24 + 116 * q^25 + 4 * q^26 + 8 * q^29 + 4 * q^30 - 4 * q^31 + 14 * q^32 + 8 * q^33 + 24 * q^34 + 124 * q^36 + 16 * q^37 - 16 * q^39 + 12 * q^40 - 12 * q^41 - 14 * q^43 + 56 * q^44 - 6 * q^45 + 52 * q^46 + 2 * q^47 - 14 * q^50 + 12 * q^51 + 24 * q^52 - 56 * q^53 + 2 * q^54 + 30 * q^55 - 2 * q^57 - 40 * q^58 + 16 * q^59 + 32 * q^60 - 14 * q^61 + 40 * q^62 + 176 * q^64 - 84 * q^65 - 12 * q^66 + 24 * q^67 - 12 * q^68 + 4 * q^69 + 48 * q^71 + 6 * q^72 - 18 * q^73 - 4 * q^74 - 8 * q^75 + 10 * q^76 + 20 * q^78 - 24 * q^79 + 88 * q^80 + 122 * q^81 + 56 * q^82 + 20 * q^83 - 54 * q^85 - 68 * q^86 + 20 * q^87 - 36 * q^88 - 40 * q^89 - 8 * q^90 - 52 * q^92 - 16 * q^93 + 24 * q^94 + 2 * q^95 + 58 * q^96 + 28 * q^97 + 6 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(2793))$ 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					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	7	19
2793.2.a.a	$2793$	$2$	2793.a	1.a	$1$	$1$	$1$	$22.302$	$\Q$	None	✓				57.2.a.b	$1$	$1$	$-2$	$-1$	$-1$	$0$		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}-q^{5}+2q^{6}+q^{9}+\cdots$
2793.2.a.b	$2793$	$2$	2793.a	1.a	$1$	$1$	$1$	$22.302$	$\Q$	None	✓				57.2.a.a	$1$	$0$	$-2$	$1$	$3$	$0$		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}+3q^{5}-2q^{6}+\cdots$
2793.2.a.c	$2793$	$2$	2793.a	1.a	$1$	$1$	$1$	$22.302$	$\Q$	None	✓				399.2.a.b	$1$	$1$	$-1$	$-1$	$-4$	$0$		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}-4q^{5}+q^{6}+3q^{8}+\cdots$
2793.2.a.d	$2793$	$2$	2793.a	1.a	$1$	$1$	$1$	$22.302$	$\Q$	None	✓	✓			2793.2.a.d	$1$	$2$	$-1$	$-1$	$-2$	$0$		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}+3q^{8}+\cdots$
2793.2.a.e	$2793$	$2$	2793.a	1.a	$1$	$1$	$1$	$22.302$	$\Q$	None	✓				399.2.a.a	$1$	$1$	$-1$	$1$	$0$	$0$		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{6}+3q^{8}+q^{9}+\cdots$
2793.2.a.f	$2793$	$2$	2793.a	1.a	$1$	$1$	$1$	$22.302$	$\Q$	None	✓	✓			2793.2.a.d	$1$	$0$	$-1$	$1$	$2$	$0$		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}+2q^{5}-q^{6}+3q^{8}+\cdots$
2793.2.a.g	$2793$	$2$	2793.a	1.a	$1$	$1$	$1$	$22.302$	$\Q$	None	✓				399.2.j.b	$1$	$1$	$0$	$-1$	$-2$	$0$		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-2q^{5}+q^{9}-3q^{11}+\cdots$
2793.2.a.h	$2793$	$2$	2793.a	1.a	$1$	$1$	$1$	$22.302$	$\Q$	None	✓				399.2.j.b	$1$	$0$	$0$	$1$	$2$	$0$		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+2q^{5}+q^{9}-3q^{11}+\cdots$
2793.2.a.i	$2793$	$2$	2793.a	1.a	$1$	$1$	$1$	$22.302$	$\Q$	None	✓				57.2.a.c	$1$	$1$	$1$	$-1$	$2$	$0$		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}+2q^{5}-q^{6}-3q^{8}+\cdots$
2793.2.a.j	$2793$	$2$	2793.a	1.a	$1$	$1$	$1$	$22.302$	$\Q$	None	✓				399.2.a.c	$1$	$0$	$1$	$1$	$0$	$0$		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{6}-3q^{8}+q^{9}+\cdots$
2793.2.a.k	$2793$	$2$	2793.a	1.a	$1$	$1$	$1$	$22.302$	$\Q$	None	✓				399.2.j.a	$1$	$1$	$2$	$-1$	$-1$	$0$		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}-q^{5}-2q^{6}+q^{9}+\cdots$
2793.2.a.l	$2793$	$2$	2793.a	1.a	$1$	$1$	$1$	$22.302$	$\Q$	None	✓				399.2.j.a	$1$	$0$	$2$	$1$	$1$	$0$		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}+q^{9}+\cdots$
2793.2.a.m	$2793$	$2$	2793.a	1.a	$1$	$2$	$2$	$22.302$	$\Q(\sqrt{2})$	None	✓	✓			2793.2.a.m	$1$	$1$	$-2$	$-2$	$0$	$0$		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}+2\beta q^{5}+\cdots$
2793.2.a.n	$2793$	$2$	2793.a	1.a	$1$	$2$	$2$	$22.302$	$\Q(\sqrt{2})$	None	✓				399.2.j.c	$1$	$1$	$-2$	$-2$	$2$	$0$		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}+(1+\cdots)q^{5}+\cdots$
2793.2.a.o	$2793$	$2$	2793.a	1.a	$1$	$2$	$2$	$22.302$	$\Q(\sqrt{2})$	None	✓				399.2.j.c	$1$	$0$	$-2$	$2$	$-2$	$0$		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}+(-1+\cdots)q^{5}+\cdots$
2793.2.a.p	$2793$	$2$	2793.a	1.a	$1$	$2$	$2$	$22.302$	$\Q(\sqrt{2})$	None	✓	✓			2793.2.a.m	$1$	$1$	$-2$	$2$	$0$	$0$		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}-2\beta q^{5}+\cdots$
2793.2.a.q	$2793$	$2$	2793.a	1.a	$1$	$2$	$2$	$22.302$	$\Q(\sqrt{3})$	None	✓	✓			2793.2.a.q	$1$	$1$	$0$	$-2$	$0$	$0$		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+q^{4}-\beta q^{6}-\beta q^{8}+q^{9}+\cdots$
2793.2.a.r	$2793$	$2$	2793.a	1.a	$1$	$2$	$2$	$22.302$	$\Q(\sqrt{3})$	None	✓	✓			2793.2.a.q	$1$	$1$	$0$	$2$	$0$	$0$		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+q^{4}+\beta q^{6}-\beta q^{8}+q^{9}+\cdots$
2793.2.a.s	$2793$	$2$	2793.a	1.a	$1$	$2$	$2$	$22.302$	$\Q(\sqrt{2})$	None	✓	✓			2793.2.a.s	$1$	$0$	$2$	$-2$	$4$	$0$		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}+2q^{5}-q^{6}-3q^{8}+\cdots$
2793.2.a.t	$2793$	$2$	2793.a	1.a	$1$	$2$	$2$	$22.302$	$\Q(\sqrt{2})$	None	✓	✓			2793.2.a.t	$1$	$0$	$2$	$-2$	$0$	$0$		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}-2\beta q^{5}+\cdots$
2793.2.a.u	$2793$	$2$	2793.a	1.a	$1$	$2$	$2$	$22.302$	$\Q(\sqrt{2})$	None	✓	✓			2793.2.a.s	$1$	$0$	$2$	$2$	$-4$	$0$		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}-2q^{5}+q^{6}-3q^{8}+\cdots$
2793.2.a.v	$2793$	$2$	2793.a	1.a	$1$	$2$	$2$	$22.302$	$\Q(\sqrt{2})$	None	✓	✓			2793.2.a.t	$1$	$0$	$2$	$2$	$0$	$0$		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}+2\beta q^{5}+\cdots$
2793.2.a.w	$2793$	$2$	2793.a	1.a	$1$	$3$	$3$	$22.302$	3.3.404.1	None	✓				399.2.a.e	$1$	$1$	$1$	$-3$	$0$	$0$		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}-q^{3}+(3+\beta _{1}-\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
2793.2.a.x	$2793$	$2$	2793.a	1.a	$1$	$3$	$3$	$22.302$	3.3.148.1	None	✓				399.2.a.d	$1$	$1$	$1$	$3$	$-4$	$0$		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
2793.2.a.y	$2793$	$2$	2793.a	1.a	$1$	$4$	$4$	$22.302$	4.4.725.1	None	✓				399.2.j.f	$1$	$0$	$-2$	$-4$	$2$	$0$		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}-q^{3}+(\beta _{2}-\beta _{3})q^{4}+(1-2\beta _{1}+\cdots)q^{5}+\cdots$
2793.2.a.z	$2793$	$2$	2793.a	1.a	$1$	$4$	$4$	$22.302$	4.4.23301.1	None	✓		✓		399.2.j.e	$1$	$1$	$-2$	$-4$	$-4$	$0$		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{3})q^{2}-q^{3}+(2-\beta _{2})q^{4}+\cdots$
2793.2.a.ba	$2793$	$2$	2793.a	1.a	$1$	$4$	$4$	$22.302$	4.4.725.1	None	✓				399.2.j.f	$1$	$1$	$-2$	$4$	$-2$	$0$		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+q^{3}+(\beta _{2}-\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots$
2793.2.a.bb	$2793$	$2$	2793.a	1.a	$1$	$4$	$4$	$22.302$	4.4.23301.1	None	✓				399.2.j.e	$1$	$0$	$-2$	$4$	$4$	$0$		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{3})q^{2}+q^{3}+(2-\beta _{2})q^{4}+\cdots$
2793.2.a.bc	$2793$	$2$	2793.a	1.a	$1$	$4$	$4$	$22.302$	4.4.1957.1	None	✓				399.2.j.d	$1$	$0$	$0$	$-4$	$4$	$0$		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots$
2793.2.a.bd	$2793$	$2$	2793.a	1.a	$1$	$4$	$4$	$22.302$	4.4.1957.1	None	✓		✓		399.2.j.d	$1$	$1$	$0$	$4$	$-4$	$0$		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots$
2793.2.a.be	$2793$	$2$	2793.a	1.a	$1$	$5$	$5$	$22.302$	5.5.1240016.1	None	✓				399.2.a.f	$1$	$0$	$1$	$-5$	$2$	$0$		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}-q^{3}+(1+\beta _{4})q^{4}-\beta _{2}q^{5}+\cdots$
2793.2.a.bf	$2793$	$2$	2793.a	1.a	$1$	$5$	$5$	$22.302$	5.5.1244416.1	None	✓	✓			2793.2.a.bf	$1$	$0$	$3$	$-5$	$2$	$0$		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-q^{3}+(2+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots$
2793.2.a.bg	$2793$	$2$	2793.a	1.a	$1$	$5$	$5$	$22.302$	5.5.368464.1	None	✓				399.2.a.g	$1$	$0$	$3$	$5$	$-4$	$0$		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
2793.2.a.bh	$2793$	$2$	2793.a	1.a	$1$	$5$	$5$	$22.302$	5.5.1244416.1	None	✓	✓			2793.2.a.bf	$1$	$0$	$3$	$5$	$-2$	$0$		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots$
2793.2.a.bi	$2793$	$2$	2793.a	1.a	$1$	$6$	$6$	$22.302$	6.6.5163008.1	None	✓	✓			2793.2.a.bi	$1$	$1$	$-2$	$-6$	$0$	$0$		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(\beta _{1}-\beta _{3}+\beta _{4})q^{4}+\cdots$
2793.2.a.bj	$2793$	$2$	2793.a	1.a	$1$	$6$	$6$	$22.302$	6.6.5163008.1	None	✓	✓	✓		2793.2.a.bi	$1$	$1$	$-2$	$6$	$0$	$0$		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(\beta _{1}-\beta _{3}+\beta _{4})q^{4}+\cdots$
2793.2.a.bk	$2793$	$2$	2793.a	1.a	$1$	$6$	$6$	$22.302$	6.6.39110656.1	None	✓	✓	✓		2793.2.a.bk	$1$	$0$	$2$	$-6$	$-4$	$0$		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}-q^{3}+(2-\beta _{1}+\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots$
2793.2.a.bl	$2793$	$2$	2793.a	1.a	$1$	$6$	$6$	$22.302$	6.6.39110656.1	None	✓	✓	✓		2793.2.a.bk	$1$	$0$	$2$	$6$	$4$	$0$		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+q^{3}+(2-\beta _{1}+\beta _{3})q^{4}+(1+\cdots)q^{5}+\cdots$
2793.2.a.bm	$2793$	$2$	2793.a	1.a	$1$	$8$	$8$	$22.302$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓		✓		399.2.j.g	$1$	$1$	$0$	$-8$	$-5$	$0$		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{5}+\cdots)q^{5}+\cdots$
2793.2.a.bn	$2793$	$2$	2793.a	1.a	$1$	$8$	$8$	$22.302$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓		✓		399.2.j.g	$1$	$0$	$0$	$8$	$5$	$0$		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{5}+\cdots)q^{5}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(2793))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_0(2793)) \simeq$ $S_{2}^{\mathrm{new}}(\Gamma_0(19))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(21))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(49))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(57))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(133))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(147))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(399))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(931))$$^{\oplus 2}$