Space of modular forms of level 1352 and weight 2

• Label: 1352.2
• Level: 1352
• Weight: 2
• Dimension: 31155
• Nonzero newspaces: 20
• Sturm bound: 227136
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 1352 = 2^{3} \cdot 13^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 20 \)
Sturm bound:			\(227136\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1352))\).

	Total	New	Old
Modular forms	58152	31973	26179
Cusp forms	55417	31155	24262
Eisenstein series	2735	818	1917

Trace form

31155 * q - 132 * q^2 - 132 * q^3 - 132 * q^4 - 132 * q^6 - 132 * q^7 - 132 * q^8 - 264 * q^9 - 132 * q^10 - 132 * q^11 - 132 * q^12 - 252 * q^14 - 132 * q^15 - 132 * q^16 - 258 * q^17 - 132 * q^18 - 108 * q^19 - 132 * q^20 + 48 * q^21 - 132 * q^22 - 108 * q^23 - 132 * q^24 - 234 * q^25 - 144 * q^26 - 180 * q^27 - 132 * q^28 + 30 * q^29 - 132 * q^30 - 108 * q^31 - 132 * q^32 - 216 * q^33 - 132 * q^34 - 108 * q^35 - 204 * q^36 + 6 * q^37 - 132 * q^38 - 156 * q^39 - 348 * q^40 - 282 * q^41 - 276 * q^42 - 228 * q^43 - 252 * q^44 - 90 * q^45 - 372 * q^46 - 204 * q^47 - 324 * q^48 - 288 * q^49 - 348 * q^50 - 300 * q^51 - 252 * q^52 - 72 * q^53 - 348 * q^54 - 276 * q^55 - 348 * q^56 - 288 * q^57 - 324 * q^58 - 204 * q^59 - 372 * q^60 - 90 * q^61 - 252 * q^62 - 180 * q^63 - 276 * q^64 - 261 * q^65 - 348 * q^66 - 108 * q^67 - 132 * q^68 + 72 * q^69 - 252 * q^70 - 36 * q^71 - 132 * q^72 - 168 * q^73 - 132 * q^74 - 84 * q^75 - 132 * q^76 + 96 * q^77 - 144 * q^78 - 204 * q^79 - 132 * q^80 - 168 * q^81 - 132 * q^82 - 12 * q^83 + 36 * q^84 + 78 * q^85 - 36 * q^86 - 180 * q^87 - 12 * q^88 - 264 * q^89 + 180 * q^90 - 216 * q^91 - 108 * q^92 - 72 * q^93 + 60 * q^94 - 324 * q^95 + 300 * q^96 - 336 * q^97 + 84 * q^98 - 516 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1352))\)

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
1352.2.a	\(\chi_{1352}(1, \cdot)\)	1352.2.a.a	1	1
		1352.2.a.b	1
		1352.2.a.c	1
		1352.2.a.d	2
		1352.2.a.e	2
		1352.2.a.f	2
		1352.2.a.g	2
		1352.2.a.h	2
		1352.2.a.i	3
		1352.2.a.j	3
		1352.2.a.k	4
		1352.2.a.l	4
		1352.2.a.m	6
		1352.2.a.n	6
1352.2.b	\(\chi_{1352}(677, \cdot)\)	n/a	144	1
1352.2.e	\(\chi_{1352}(1013, \cdot)\)	n/a	144	1
1352.2.f	\(\chi_{1352}(337, \cdot)\)	1352.2.f.a	2	1
		1352.2.f.b	2
		1352.2.f.c	4
		1352.2.f.d	4
		1352.2.f.e	6
		1352.2.f.f	8
		1352.2.f.g	12
1352.2.i	\(\chi_{1352}(529, \cdot)\)	1352.2.i.a	2	2
		1352.2.i.b	2
		1352.2.i.c	2
		1352.2.i.d	4
		1352.2.i.e	4
		1352.2.i.f	4
		1352.2.i.g	4
		1352.2.i.h	4
		1352.2.i.i	6
		1352.2.i.j	6
		1352.2.i.k	8
		1352.2.i.l	8
		1352.2.i.m	12
		1352.2.i.n	12
1352.2.k	\(\chi_{1352}(239, \cdot)\)	None	0	2
1352.2.m	\(\chi_{1352}(99, \cdot)\)	n/a	288	2
1352.2.o	\(\chi_{1352}(361, \cdot)\)	1352.2.o.a	4	2
		1352.2.o.b	4
		1352.2.o.c	8
		1352.2.o.d	8
		1352.2.o.e	8
		1352.2.o.f	8
		1352.2.o.g	12
		1352.2.o.h	24
1352.2.r	\(\chi_{1352}(653, \cdot)\)	n/a	288	2
1352.2.s	\(\chi_{1352}(485, \cdot)\)	n/a	288	2
1352.2.u	\(\chi_{1352}(19, \cdot)\)	n/a	576	4
1352.2.w	\(\chi_{1352}(319, \cdot)\)	None	0	4
1352.2.y	\(\chi_{1352}(105, \cdot)\)	n/a	540	12
1352.2.bb	\(\chi_{1352}(25, \cdot)\)	n/a	552	12
1352.2.bc	\(\chi_{1352}(77, \cdot)\)	n/a	2160	12
1352.2.bf	\(\chi_{1352}(53, \cdot)\)	n/a	2160	12
1352.2.bg	\(\chi_{1352}(9, \cdot)\)	n/a	1080	24
1352.2.bi	\(\chi_{1352}(83, \cdot)\)	n/a	4320	24
1352.2.bk	\(\chi_{1352}(31, \cdot)\)	None	0	24
1352.2.bm	\(\chi_{1352}(69, \cdot)\)	n/a	4320	24
1352.2.bn	\(\chi_{1352}(29, \cdot)\)	n/a	4320	24
1352.2.bq	\(\chi_{1352}(17, \cdot)\)	n/a	1104	24
1352.2.bs	\(\chi_{1352}(7, \cdot)\)	None	0	48
1352.2.bu	\(\chi_{1352}(11, \cdot)\)	n/a	8640	48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1352))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1352)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(676))\)\(^{\oplus 2}\)