Space of modular forms of level 152 and weight 2

• Label: 152.2
• Level: 152
• Weight: 2
• Dimension: 369
• Nonzero newspaces: 9
• Newform subspaces: 21
• Sturm bound: 2880
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 9 \)
Newform subspaces:			\( 21 \)
Sturm bound:			\(2880\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(152))\).

	Total	New	Old
Modular forms	828	437	391
Cusp forms	613	369	244
Eisenstein series	215	68	147

Trace form

369 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^19 - 36 * q^20 - 18 * q^22 - 18 * q^23 - 18 * q^24 - 36 * q^25 - 18 * q^26 - 27 * q^27 - 18 * q^28 - 18 * q^29 - 18 * q^30 - 36 * q^31 - 18 * q^32 - 90 * q^33 - 18 * q^34 - 54 * q^35 - 18 * q^36 - 18 * q^37 - 18 * q^38 - 90 * q^39 - 18 * q^40 - 54 * q^41 - 18 * q^42 - 54 * q^43 - 18 * q^44 - 54 * q^45 - 18 * q^46 - 36 * q^47 - 18 * q^48 - 54 * q^49 - 18 * q^50 - 27 * q^51 - 18 * q^52 + 36 * q^54 - 18 * q^55 - 18 * q^56 - 36 * q^57 - 36 * q^58 - 18 * q^59 + 18 * q^60 + 18 * q^61 + 72 * q^62 + 54 * q^63 + 126 * q^64 + 18 * q^65 + 126 * q^66 + 90 * q^67 + 108 * q^68 + 198 * q^70 + 36 * q^71 + 252 * q^72 + 45 * q^73 + 126 * q^74 + 126 * q^75 + 162 * q^76 + 54 * q^77 + 162 * q^78 + 108 * q^79 + 126 * q^80 + 45 * q^81 + 252 * q^82 + 36 * q^83 + 198 * q^84 + 108 * q^86 + 90 * q^87 + 126 * q^88 + 18 * q^89 + 126 * q^90 + 54 * q^91 + 72 * q^92 + 18 * q^93 + 18 * q^94 - 54 * q^95 - 36 * q^96 - 72 * q^97 - 18 * q^98 - 81 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(152))\)

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
152.2.a	\(\chi_{152}(1, \cdot)\)	152.2.a.a	1	1
		152.2.a.b	1
		152.2.a.c	3
152.2.b	\(\chi_{152}(75, \cdot)\)	152.2.b.a	2	1
		152.2.b.b	4
		152.2.b.c	12
152.2.c	\(\chi_{152}(77, \cdot)\)	152.2.c.a	2	1
		152.2.c.b	16
152.2.h	\(\chi_{152}(151, \cdot)\)	None	0	1
152.2.i	\(\chi_{152}(49, \cdot)\)	152.2.i.a	2	2
		152.2.i.b	2
		152.2.i.c	6
152.2.j	\(\chi_{152}(31, \cdot)\)	None	0	2
152.2.o	\(\chi_{152}(27, \cdot)\)	152.2.o.a	4	2
		152.2.o.b	4
		152.2.o.c	28
152.2.p	\(\chi_{152}(45, \cdot)\)	152.2.p.a	36	2
152.2.q	\(\chi_{152}(9, \cdot)\)	152.2.q.a	6	6
		152.2.q.b	6
		152.2.q.c	18
152.2.t	\(\chi_{152}(5, \cdot)\)	152.2.t.a	108	6
152.2.v	\(\chi_{152}(3, \cdot)\)	152.2.v.a	12	6
		152.2.v.b	96
152.2.w	\(\chi_{152}(15, \cdot)\)	None	0	6

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(152))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(152)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 2}\)