Space of modular forms of level 155 and weight 2

• Label: 155.2
• Level: 155
• Weight: 2
• Dimension: 789
• Nonzero newspaces: 12
• Newform subspaces: 25
• Sturm bound: 3840
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 155 = 5 \cdot 31 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 25 \)
Sturm bound:			\(3840\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(155))\).

	Total	New	Old
Modular forms	1080	965	115
Cusp forms	841	789	52
Eisenstein series	239	176	63

Trace form

789 * q - 33 * q^2 - 34 * q^3 - 37 * q^4 - 46 * q^5 - 102 * q^6 - 38 * q^7 - 45 * q^8 - 43 * q^9 - 48 * q^10 - 102 * q^11 - 58 * q^12 - 44 * q^13 - 54 * q^14 - 49 * q^15 - 121 * q^16 - 48 * q^17 - 69 * q^18 - 50 * q^19 - 52 * q^20 - 112 * q^21 - 6 * q^22 - 24 * q^23 + 30 * q^24 - 36 * q^25 - 72 * q^26 + 20 * q^27 + 74 * q^28 + 18 * q^30 - 61 * q^31 + 57 * q^32 - 18 * q^33 + 36 * q^34 - 23 * q^35 - 21 * q^36 + 22 * q^37 - 30 * q^38 - 16 * q^39 - 102 * q^41 - 66 * q^42 - 64 * q^43 - 114 * q^44 - 58 * q^45 - 162 * q^46 - 78 * q^47 - 64 * q^48 - 27 * q^49 + 27 * q^50 + 18 * q^51 + 22 * q^52 - 24 * q^53 + 180 * q^54 + 3 * q^55 + 60 * q^56 + 70 * q^57 + 90 * q^58 - 30 * q^59 + 182 * q^60 + 58 * q^61 + 57 * q^62 + 76 * q^63 + 83 * q^64 + 31 * q^65 + 216 * q^66 - 38 * q^67 + 54 * q^68 + 54 * q^69 + 66 * q^70 - 42 * q^71 + 105 * q^72 - 44 * q^73 + 6 * q^74 + 56 * q^75 + 20 * q^76 + 24 * q^77 + 72 * q^78 - 40 * q^79 + 74 * q^80 - 91 * q^81 - 36 * q^82 + 96 * q^83 + 106 * q^84 - 3 * q^85 + 18 * q^86 - 30 * q^87 + 150 * q^88 + 30 * q^89 + 141 * q^90 - 72 * q^91 + 192 * q^92 + 86 * q^93 - 84 * q^94 + 55 * q^95 + 108 * q^96 + 2 * q^97 + 159 * q^98 - 36 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(155))\)

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
155.2.a	\(\chi_{155}(1, \cdot)\)	155.2.a.a	1	1
		155.2.a.b	1
		155.2.a.c	1
		155.2.a.d	4
		155.2.a.e	4
155.2.b	\(\chi_{155}(94, \cdot)\)	155.2.b.a	4	1
		155.2.b.b	10
155.2.e	\(\chi_{155}(36, \cdot)\)	155.2.e.a	2	2
		155.2.e.b	2
		155.2.e.c	8
		155.2.e.d	8
155.2.f	\(\chi_{155}(92, \cdot)\)	155.2.f.a	12	2
		155.2.f.b	16
155.2.h	\(\chi_{155}(16, \cdot)\)	155.2.h.a	24	4
		155.2.h.b	24
155.2.j	\(\chi_{155}(129, \cdot)\)	155.2.j.a	28	2
155.2.n	\(\chi_{155}(4, \cdot)\)	155.2.n.a	56	4
155.2.p	\(\chi_{155}(37, \cdot)\)	155.2.p.a	4	4
		155.2.p.b	4
		155.2.p.c	48
155.2.q	\(\chi_{155}(41, \cdot)\)	155.2.q.a	40	8
		155.2.q.b	40
155.2.r	\(\chi_{155}(23, \cdot)\)	155.2.r.a	112	8
155.2.u	\(\chi_{155}(9, \cdot)\)	155.2.u.a	112	8
155.2.x	\(\chi_{155}(3, \cdot)\)	155.2.x.a	224	16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(155))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(155)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(155))\)\(^{\oplus 1}\)