Space of modular forms of level 352 and weight 2

• Label: 352.2
• Level: 352
• Weight: 2
• Dimension: 2034
• Nonzero newspaces: 12
• Newform subspaces: 26
• Sturm bound: 15360
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 352 = 2^{5} \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 26 \)
Sturm bound:			\(15360\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(352))\).

	Total	New	Old
Modular forms	4160	2214	1946
Cusp forms	3521	2034	1487
Eisenstein series	639	180	459

Trace form

2034 * q - 32 * q^2 - 22 * q^3 - 32 * q^4 - 28 * q^5 - 32 * q^6 - 22 * q^7 - 32 * q^8 - 46 * q^9 - 48 * q^10 - 26 * q^11 - 104 * q^12 - 44 * q^13 - 64 * q^14 - 30 * q^15 - 72 * q^16 - 24 * q^17 - 72 * q^18 - 22 * q^19 - 64 * q^20 - 32 * q^21 - 48 * q^22 - 68 * q^23 - 8 * q^24 - 50 * q^25 + 8 * q^26 - 70 * q^27 + 8 * q^28 - 12 * q^29 + 32 * q^30 - 62 * q^31 + 8 * q^32 - 92 * q^33 - 48 * q^34 - 70 * q^35 + 24 * q^36 - 28 * q^37 - 48 * q^38 - 70 * q^39 - 56 * q^40 - 72 * q^41 - 72 * q^42 - 48 * q^43 - 76 * q^44 - 108 * q^45 - 96 * q^46 - 30 * q^47 - 136 * q^48 - 6 * q^49 - 112 * q^50 - 14 * q^51 - 48 * q^52 - 92 * q^53 - 56 * q^54 + 6 * q^55 - 96 * q^56 - 52 * q^57 - 24 * q^58 + 42 * q^59 - 24 * q^60 - 76 * q^61 + 8 * q^62 + 36 * q^63 + 40 * q^64 - 60 * q^65 - 12 * q^66 + 28 * q^67 - 72 * q^68 - 96 * q^69 - 8 * q^70 + 22 * q^71 - 80 * q^72 - 120 * q^73 - 64 * q^74 - 78 * q^75 - 32 * q^76 - 132 * q^77 - 152 * q^78 - 130 * q^79 - 24 * q^80 - 158 * q^81 - 32 * q^82 - 202 * q^83 - 72 * q^84 - 224 * q^85 + 8 * q^86 - 244 * q^87 - 40 * q^88 - 212 * q^89 - 56 * q^90 - 238 * q^91 + 40 * q^92 - 168 * q^93 - 56 * q^94 - 242 * q^95 - 40 * q^96 - 240 * q^97 + 8 * q^98 - 178 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(352))\)

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
352.2.a	\(\chi_{352}(1, \cdot)\)	352.2.a.a	1	1
		352.2.a.b	1
		352.2.a.c	1
		352.2.a.d	1
		352.2.a.e	1
		352.2.a.f	1
		352.2.a.g	2
		352.2.a.h	2
352.2.c	\(\chi_{352}(177, \cdot)\)	352.2.c.a	10	1
352.2.e	\(\chi_{352}(351, \cdot)\)	352.2.e.a	12	1
352.2.g	\(\chi_{352}(175, \cdot)\)	352.2.g.a	2	1
		352.2.g.b	8
352.2.i	\(\chi_{352}(87, \cdot)\)	None	0	2
352.2.j	\(\chi_{352}(89, \cdot)\)	None	0	2
352.2.m	\(\chi_{352}(97, \cdot)\)	352.2.m.a	4	4
		352.2.m.b	4
		352.2.m.c	8
		352.2.m.d	8
		352.2.m.e	12
		352.2.m.f	12
352.2.n	\(\chi_{352}(45, \cdot)\)	352.2.n.a	160	4
352.2.q	\(\chi_{352}(43, \cdot)\)	352.2.q.a	184	4
352.2.s	\(\chi_{352}(79, \cdot)\)	352.2.s.a	8	4
		352.2.s.b	32
352.2.u	\(\chi_{352}(63, \cdot)\)	352.2.u.a	48	4
352.2.w	\(\chi_{352}(49, \cdot)\)	352.2.w.a	40	4
352.2.ba	\(\chi_{352}(9, \cdot)\)	None	0	8
352.2.bb	\(\chi_{352}(7, \cdot)\)	None	0	8
352.2.bc	\(\chi_{352}(19, \cdot)\)	352.2.bc.a	736	16
352.2.bf	\(\chi_{352}(5, \cdot)\)	352.2.bf.a	736	16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(352))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(352)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 2}\)