Space of modular forms of level 2793 and weight 1

• Label: 2793.1
• Level: 2793
• Weight: 1
• Dimension: 298
• Nonzero newspaces: 19
• Newform subspaces: 35
• Sturm bound: 564480
• Trace bound: 43

Defining parameters

Level:	\( N \)	=	\( 2793 = 3 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	=	\( 1 \)
Nonzero newspaces:			\( 19 \)
Newform subspaces:			\( 35 \)
Sturm bound:			\(564480\)
Trace bound:			\(43\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2793))\).

	Total	New	Old
Modular forms	4804	1946	2858
Cusp forms	484	298	186
Eisenstein series	4320	1648	2672

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	282	16	0	0

Trace form

298 * q + 3 * q^3 - q^4 - 4 * q^6 + 2 * q^7 + q^9 + 2 * q^10 + 6 * q^12 + 13 * q^13 + 8 * q^15 + 9 * q^16 + 8 * q^19 + 2 * q^21 + 8 * q^22 + 2 * q^24 - q^25 + 6 * q^27 + 2 * q^28 + 8 * q^30 + 10 * q^31 + 2 * q^33 + 5 * q^36 - 12 * q^37 - 8 * q^39 + 2 * q^40 - 11 * q^43 - 11 * q^48 + 2 * q^49 - 5 * q^52 - 2 * q^54 - 4 * q^55 - 11 * q^57 + 4 * q^58 - 5 * q^61 - 12 * q^63 - 24 * q^64 + 7 * q^67 + 9 * q^73 + 6 * q^75 + 3 * q^76 + 8 * q^78 + 11 * q^79 - 3 * q^81 + 2 * q^82 + 2 * q^84 - 16 * q^85 - 4 * q^87 - 4 * q^88 + 4 * q^90 + 4 * q^91 + 9 * q^93 - 8 * q^94 + 10 * q^97

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2793))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
2793.1.b	\(\chi_{2793}(932, \cdot)\)	None	0	1
2793.1.e	\(\chi_{2793}(1177, \cdot)\)	None	0	1
2793.1.g	\(\chi_{2793}(685, \cdot)\)	None	0	1
2793.1.h	\(\chi_{2793}(2792, \cdot)\)	None	0	1
2793.1.n	\(\chi_{2793}(410, \cdot)\)	2793.1.n.a	2	2
		2793.1.n.b	2
		2793.1.n.c	4
2793.1.o	\(\chi_{2793}(373, \cdot)\)	None	0	2
2793.1.q	\(\chi_{2793}(293, \cdot)\)	None	0	2
2793.1.r	\(\chi_{2793}(962, \cdot)\)	2793.1.r.a	2	2
		2793.1.r.b	2
2793.1.s	\(\chi_{2793}(227, \cdot)\)	2793.1.s.a	2	2
		2793.1.s.b	2
		2793.1.s.c	4
		2793.1.s.d	4
2793.1.u	\(\chi_{2793}(913, \cdot)\)	None	0	2
2793.1.v	\(\chi_{2793}(178, \cdot)\)	None	0	2
2793.1.y	\(\chi_{2793}(391, \cdot)\)	None	0	2
2793.1.ba	\(\chi_{2793}(949, \cdot)\)	None	0	2
2793.1.bb	\(\chi_{2793}(1684, \cdot)\)	None	0	2
2793.1.be	\(\chi_{2793}(1471, \cdot)\)	None	0	2
2793.1.bf	\(\chi_{2793}(197, \cdot)\)	2793.1.bf.a	2	2
		2793.1.bf.b	4
		2793.1.bf.c	4
2793.1.bi	\(\chi_{2793}(1892, \cdot)\)	2793.1.bi.a	2	2
		2793.1.bi.b	2
		2793.1.bi.c	4
2793.1.bj	\(\chi_{2793}(704, \cdot)\)	None	0	2
2793.1.bl	\(\chi_{2793}(619, \cdot)\)	None	0	2
2793.1.bn	\(\chi_{2793}(521, \cdot)\)	2793.1.bn.a	2	2
		2793.1.bn.b	2
2793.1.bs	\(\chi_{2793}(398, \cdot)\)	2793.1.bs.a	6	6
		2793.1.bs.b	6
2793.1.bt	\(\chi_{2793}(286, \cdot)\)	None	0	6
2793.1.bv	\(\chi_{2793}(379, \cdot)\)	None	0	6
2793.1.by	\(\chi_{2793}(134, \cdot)\)	None	0	6
2793.1.ca	\(\chi_{2793}(374, \cdot)\)	2793.1.ca.a	6	6
2793.1.cb	\(\chi_{2793}(313, \cdot)\)	None	0	6
2793.1.cc	\(\chi_{2793}(244, \cdot)\)	None	0	6
2793.1.cf	\(\chi_{2793}(146, \cdot)\)	2793.1.cf.a	6	6
		2793.1.cf.b	6
2793.1.cg	\(\chi_{2793}(509, \cdot)\)	2793.1.cg.a	6	6
2793.1.ch	\(\chi_{2793}(766, \cdot)\)	None	0	6
2793.1.ci	\(\chi_{2793}(557, \cdot)\)	2793.1.ci.a	6	6
2793.1.cm	\(\chi_{2793}(508, \cdot)\)	None	0	6
2793.1.cn	\(\chi_{2793}(148, \cdot)\)	None	0	6
2793.1.co	\(\chi_{2793}(491, \cdot)\)	2793.1.co.a	6	6
		2793.1.co.b	6
2793.1.cp	\(\chi_{2793}(263, \cdot)\)	2793.1.cp.a	6	6
2793.1.ct	\(\chi_{2793}(67, \cdot)\)	None	0	6
2793.1.cy	\(\chi_{2793}(122, \cdot)\)	None	0	12
2793.1.da	\(\chi_{2793}(220, \cdot)\)	None	0	12
2793.1.dc	\(\chi_{2793}(191, \cdot)\)	None	0	12
2793.1.dd	\(\chi_{2793}(296, \cdot)\)	None	0	12
2793.1.dg	\(\chi_{2793}(239, \cdot)\)	2793.1.dg.a	12	12
		2793.1.dg.b	12
2793.1.dh	\(\chi_{2793}(274, \cdot)\)	None	0	12
2793.1.dk	\(\chi_{2793}(88, \cdot)\)	None	0	12
2793.1.dl	\(\chi_{2793}(37, \cdot)\)	None	0	12
2793.1.dn	\(\chi_{2793}(349, \cdot)\)	None	0	12
2793.1.dq	\(\chi_{2793}(334, \cdot)\)	None	0	12
2793.1.dr	\(\chi_{2793}(115, \cdot)\)	None	0	12
2793.1.dt	\(\chi_{2793}(341, \cdot)\)	None	0	12
2793.1.du	\(\chi_{2793}(164, \cdot)\)	None	0	12
2793.1.dv	\(\chi_{2793}(335, \cdot)\)	2793.1.dv.a	12	12
		2793.1.dv.b	12
2793.1.dx	\(\chi_{2793}(46, \cdot)\)	None	0	12
2793.1.dy	\(\chi_{2793}(11, \cdot)\)	None	0	12
2793.1.ed	\(\chi_{2793}(268, \cdot)\)	None	0	36
2793.1.eh	\(\chi_{2793}(92, \cdot)\)	None	0	36
2793.1.ei	\(\chi_{2793}(23, \cdot)\)	2793.1.ei.a	36	36
2793.1.ej	\(\chi_{2793}(109, \cdot)\)	None	0	36
2793.1.ek	\(\chi_{2793}(22, \cdot)\)	None	0	36
2793.1.eo	\(\chi_{2793}(137, \cdot)\)	2793.1.eo.a	36	36
2793.1.ep	\(\chi_{2793}(187, \cdot)\)	None	0	36
2793.1.eq	\(\chi_{2793}(41, \cdot)\)	None	0	36
2793.1.er	\(\chi_{2793}(59, \cdot)\)	2793.1.er.a	36	36
2793.1.eu	\(\chi_{2793}(61, \cdot)\)	None	0	36
2793.1.ev	\(\chi_{2793}(55, \cdot)\)	None	0	36
2793.1.ew	\(\chi_{2793}(143, \cdot)\)	2793.1.ew.a	36	36

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2793))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2793)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(133))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(399))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(931))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2793))\)\(^{\oplus 1}\)