Space of modular forms of level 1936 and weight 4

• Label: 1936.4
• Level: 1936
• Weight: 4
• Dimension: 192161
• Nonzero newspaces: 16
• Sturm bound: 929280
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 1936 = 2^{4} \cdot 11^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(929280\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1936))\).

	Total	New	Old
Modular forms	350720	193426	157294
Cusp forms	346240	192161	154079
Eisenstein series	4480	1265	3215

Trace form

192161 * q - 182 * q^2 - 133 * q^3 - 172 * q^4 - 229 * q^5 - 212 * q^6 - 159 * q^7 - 224 * q^8 - 56 * q^9 - 248 * q^10 - 150 * q^11 - 240 * q^12 - 205 * q^13 + 8 * q^14 - 267 * q^15 + 100 * q^16 - 359 * q^17 - 6 * q^18 - 205 * q^19 - 376 * q^20 - 259 * q^21 - 200 * q^22 - 199 * q^23 - 1028 * q^24 - 166 * q^25 - 444 * q^26 - 103 * q^27 + 100 * q^28 - 229 * q^29 + 1056 * q^30 + 393 * q^31 + 788 * q^32 + 890 * q^33 + 96 * q^34 + 2129 * q^35 - 776 * q^36 - 437 * q^37 - 1412 * q^38 - 2807 * q^39 - 1516 * q^40 - 3203 * q^41 - 860 * q^42 - 3615 * q^43 - 200 * q^44 - 5129 * q^45 + 952 * q^46 - 3467 * q^47 + 1588 * q^48 - 1118 * q^49 + 546 * q^50 + 125 * q^51 - 416 * q^52 + 1035 * q^53 - 1556 * q^54 + 2520 * q^55 - 828 * q^56 + 5339 * q^57 - 172 * q^58 + 2239 * q^59 - 372 * q^60 + 1235 * q^61 - 260 * q^62 + 2487 * q^63 + 332 * q^64 - 931 * q^65 - 200 * q^66 + 1499 * q^67 - 1060 * q^68 + 849 * q^69 - 13740 * q^70 - 4563 * q^71 - 29688 * q^72 - 19571 * q^73 - 19632 * q^74 - 9093 * q^75 - 15808 * q^76 - 2090 * q^77 - 2552 * q^78 - 2395 * q^79 + 10812 * q^80 + 10566 * q^81 + 21916 * q^82 + 3767 * q^83 + 37780 * q^84 + 25583 * q^85 + 30784 * q^86 + 11047 * q^87 + 27640 * q^88 + 14229 * q^89 + 53556 * q^90 + 11669 * q^91 + 21892 * q^92 + 16463 * q^93 + 18172 * q^94 + 9953 * q^95 + 1388 * q^96 - 1607 * q^97 - 9986 * q^98 - 2400 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1936))\)

We only show spaces with even 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
1936.4.a	\(\chi_{1936}(1, \cdot)\)	1936.4.a.a	1	1
		1936.4.a.b	1
		1936.4.a.c	1
		1936.4.a.d	1
		1936.4.a.e	1
		1936.4.a.f	1
		1936.4.a.g	1
		1936.4.a.h	1
		1936.4.a.i	1
		1936.4.a.j	1
		1936.4.a.k	1
		1936.4.a.l	1
		1936.4.a.m	1
		1936.4.a.n	1
		1936.4.a.o	2
		1936.4.a.p	2
		1936.4.a.q	2
		1936.4.a.r	2
		1936.4.a.s	2
		1936.4.a.t	2
		1936.4.a.u	2
		1936.4.a.v	2
		1936.4.a.w	2
		1936.4.a.x	2
		1936.4.a.y	2
		1936.4.a.z	2
		1936.4.a.ba	2
		1936.4.a.bb	2
		1936.4.a.bc	2
		1936.4.a.bd	3
		1936.4.a.be	3
		1936.4.a.bf	3
		1936.4.a.bg	3
		1936.4.a.bh	3
		1936.4.a.bi	3
		1936.4.a.bj	3
		1936.4.a.bk	4
		1936.4.a.bl	4
		1936.4.a.bm	4
		1936.4.a.bn	4
		1936.4.a.bo	4
		1936.4.a.bp	4
		1936.4.a.bq	6
		1936.4.a.br	6
		1936.4.a.bs	6
		1936.4.a.bt	8
		1936.4.a.bu	8
		1936.4.a.bv	8
		1936.4.a.bw	8
		1936.4.a.bx	10
		1936.4.a.by	10
1936.4.c	\(\chi_{1936}(969, \cdot)\)	None	0	1
1936.4.e	\(\chi_{1936}(1935, \cdot)\)	n/a	162	1
1936.4.g	\(\chi_{1936}(967, \cdot)\)	None	0	1
1936.4.i	\(\chi_{1936}(483, \cdot)\)	n/a	1280	2
1936.4.j	\(\chi_{1936}(485, \cdot)\)	n/a	1290	2
1936.4.m	\(\chi_{1936}(81, \cdot)\)	n/a	632	4
1936.4.o	\(\chi_{1936}(215, \cdot)\)	None	0	4
1936.4.q	\(\chi_{1936}(239, \cdot)\)	n/a	648	4
1936.4.s	\(\chi_{1936}(9, \cdot)\)	None	0	4
1936.4.u	\(\chi_{1936}(177, \cdot)\)	n/a	1970	10
1936.4.x	\(\chi_{1936}(245, \cdot)\)	n/a	5120	8
1936.4.y	\(\chi_{1936}(403, \cdot)\)	n/a	5120	8
1936.4.z	\(\chi_{1936}(175, \cdot)\)	n/a	1980	10
1936.4.bb	\(\chi_{1936}(89, \cdot)\)	None	0	10
1936.4.be	\(\chi_{1936}(87, \cdot)\)	None	0	10
1936.4.bi	\(\chi_{1936}(45, \cdot)\)	n/a	15800	20
1936.4.bj	\(\chi_{1936}(43, \cdot)\)	n/a	15800	20
1936.4.bk	\(\chi_{1936}(49, \cdot)\)	n/a	7880	40
1936.4.bm	\(\chi_{1936}(7, \cdot)\)	None	0	40
1936.4.bp	\(\chi_{1936}(25, \cdot)\)	None	0	40
1936.4.br	\(\chi_{1936}(63, \cdot)\)	n/a	7920	40
1936.4.bs	\(\chi_{1936}(19, \cdot)\)	n/a	63200	80
1936.4.bt	\(\chi_{1936}(5, \cdot)\)	n/a	63200	80

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1936))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1936)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 15}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(484))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(968))\)\(^{\oplus 2}\)