Space of modular forms of level 1936 and weight 2

• Label: 1936.2
• Level: 1936
• Weight: 2
• Dimension: 63632
• Nonzero newspaces: 16
• Sturm bound: 464640
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 1936 = 2^{4} \cdot 11^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(464640\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1936))\).

	Total	New	Old
Modular forms	118400	64897	53503
Cusp forms	113921	63632	50289
Eisenstein series	4479	1265	3214

Trace form

63632 * q - 182 * q^2 - 137 * q^3 - 180 * q^4 - 227 * q^5 - 176 * q^6 - 135 * q^7 - 176 * q^8 - 45 * q^9 - 180 * q^10 - 150 * q^11 - 344 * q^12 - 227 * q^13 - 184 * q^14 - 131 * q^15 - 188 * q^16 - 409 * q^17 - 178 * q^18 - 129 * q^19 - 176 * q^20 - 211 * q^21 - 200 * q^22 - 255 * q^23 - 180 * q^24 - 45 * q^25 - 176 * q^26 - 143 * q^27 - 172 * q^28 - 219 * q^29 - 184 * q^30 - 151 * q^31 - 172 * q^32 - 430 * q^33 - 336 * q^34 - 79 * q^35 - 184 * q^36 - 179 * q^37 - 192 * q^38 - 15 * q^39 - 188 * q^40 + 35 * q^41 - 180 * q^42 - 75 * q^43 - 200 * q^44 - 303 * q^45 - 168 * q^46 - 59 * q^47 - 172 * q^48 - 319 * q^49 - 186 * q^50 - 11 * q^51 - 184 * q^52 - 195 * q^53 - 180 * q^54 - 120 * q^55 - 348 * q^56 - 5 * q^57 - 192 * q^58 - 141 * q^59 - 180 * q^60 - 243 * q^61 - 164 * q^62 - 161 * q^63 - 180 * q^64 - 391 * q^65 - 200 * q^66 - 265 * q^67 - 180 * q^68 - 207 * q^69 - 452 * q^70 - 155 * q^71 - 376 * q^72 - 205 * q^73 - 380 * q^74 - 209 * q^75 - 488 * q^76 - 330 * q^77 - 824 * q^78 - 235 * q^79 - 612 * q^80 - 635 * q^81 - 580 * q^82 - 237 * q^83 - 668 * q^84 - 541 * q^85 - 500 * q^86 - 305 * q^87 - 520 * q^88 - 245 * q^89 - 824 * q^90 - 251 * q^91 - 524 * q^92 - 529 * q^93 - 676 * q^94 - 247 * q^95 - 596 * q^96 - 649 * q^97 - 626 * q^98 - 200 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1936))\)

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
1936.2.a	\(\chi_{1936}(1, \cdot)\)	1936.2.a.a	1	1
		1936.2.a.b	1
		1936.2.a.c	1
		1936.2.a.d	1
		1936.2.a.e	1
		1936.2.a.f	1
		1936.2.a.g	1
		1936.2.a.h	1
		1936.2.a.i	1
		1936.2.a.j	1
		1936.2.a.k	1
		1936.2.a.l	1
		1936.2.a.m	2
		1936.2.a.n	2
		1936.2.a.o	2
		1936.2.a.p	2
		1936.2.a.q	2
		1936.2.a.r	2
		1936.2.a.s	2
		1936.2.a.t	2
		1936.2.a.u	2
		1936.2.a.v	2
		1936.2.a.w	2
		1936.2.a.x	2
		1936.2.a.y	2
		1936.2.a.z	2
		1936.2.a.ba	2
		1936.2.a.bb	4
		1936.2.a.bc	4
1936.2.c	\(\chi_{1936}(969, \cdot)\)	None	0	1
1936.2.e	\(\chi_{1936}(1935, \cdot)\)	1936.2.e.a	2	1
		1936.2.e.b	4
		1936.2.e.c	4
		1936.2.e.d	4
		1936.2.e.e	8
		1936.2.e.f	16
		1936.2.e.g	16
1936.2.g	\(\chi_{1936}(967, \cdot)\)	None	0	1
1936.2.i	\(\chi_{1936}(483, \cdot)\)	n/a	416	2
1936.2.j	\(\chi_{1936}(485, \cdot)\)	n/a	418	2
1936.2.m	\(\chi_{1936}(81, \cdot)\)	n/a	200	4
1936.2.o	\(\chi_{1936}(215, \cdot)\)	None	0	4
1936.2.q	\(\chi_{1936}(239, \cdot)\)	n/a	216	4
1936.2.s	\(\chi_{1936}(9, \cdot)\)	None	0	4
1936.2.u	\(\chi_{1936}(177, \cdot)\)	n/a	650	10
1936.2.x	\(\chi_{1936}(245, \cdot)\)	n/a	1664	8
1936.2.y	\(\chi_{1936}(403, \cdot)\)	n/a	1664	8
1936.2.z	\(\chi_{1936}(175, \cdot)\)	n/a	660	10
1936.2.bb	\(\chi_{1936}(89, \cdot)\)	None	0	10
1936.2.be	\(\chi_{1936}(87, \cdot)\)	None	0	10
1936.2.bi	\(\chi_{1936}(45, \cdot)\)	n/a	5240	20
1936.2.bj	\(\chi_{1936}(43, \cdot)\)	n/a	5240	20
1936.2.bk	\(\chi_{1936}(49, \cdot)\)	n/a	2600	40
1936.2.bm	\(\chi_{1936}(7, \cdot)\)	None	0	40
1936.2.bp	\(\chi_{1936}(25, \cdot)\)	None	0	40
1936.2.br	\(\chi_{1936}(63, \cdot)\)	n/a	2640	40
1936.2.bs	\(\chi_{1936}(19, \cdot)\)	n/a	20960	80
1936.2.bt	\(\chi_{1936}(5, \cdot)\)	n/a	20960	80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1936))\) into lower level spaces

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