Space of modular forms of level 145 and weight 2

• Label: 145.2
• Level: 145
• Weight: 2
• Dimension: 685
• Nonzero newspaces: 12
• Newform subspaces: 22
• Sturm bound: 3360
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 145 = 5 \cdot 29 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 22 \)
Sturm bound:			\(3360\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(145))\).

	Total	New	Old
Modular forms	952	849	103
Cusp forms	729	685	44
Eisenstein series	223	164	59

Trace form

685 * q - 31 * q^2 - 32 * q^3 - 35 * q^4 - 43 * q^5 - 96 * q^6 - 36 * q^7 - 43 * q^8 - 41 * q^9 - 45 * q^10 - 96 * q^11 - 56 * q^12 - 42 * q^13 - 52 * q^14 - 46 * q^15 - 115 * q^16 - 46 * q^17 - 67 * q^18 - 48 * q^19 - 28 * q^20 - 60 * q^21 - 8 * q^22 - 24 * q^23 + 80 * q^24 - 15 * q^25 - 56 * q^26 + 16 * q^27 + 56 * q^28 - q^29 - 12 * q^30 - 60 * q^31 + 21 * q^32 + 8 * q^33 - 12 * q^34 - 22 * q^35 - 7 * q^36 - 38 * q^37 - 32 * q^38 - 28 * q^39 - 36 * q^40 - 126 * q^41 - 124 * q^42 - 72 * q^43 - 84 * q^44 - 20 * q^45 - 16 * q^46 - 20 * q^47 + 72 * q^48 + 27 * q^49 + 53 * q^50 - 44 * q^51 + 98 * q^52 + 44 * q^53 + 104 * q^54 + 58 * q^55 + 48 * q^56 + 32 * q^57 + 221 * q^58 - 60 * q^59 + 126 * q^60 - 34 * q^61 + 72 * q^62 + 92 * q^63 + 97 * q^64 + 7 * q^65 - 4 * q^66 + 16 * q^67 + 42 * q^68 - 12 * q^69 + 74 * q^70 - 16 * q^71 + 85 * q^72 + 24 * q^73 + 54 * q^74 + 24 * q^75 + 16 * q^77 + 28 * q^78 - 52 * q^79 + 123 * q^80 + 19 * q^81 - 42 * q^82 + 168 * q^84 + 24 * q^85 + 92 * q^86 - 4 * q^87 + 100 * q^88 + 22 * q^89 + 101 * q^90 - 28 * q^91 + 140 * q^92 - 44 * q^93 - 60 * q^94 + 50 * q^95 + 140 * q^96 + 28 * q^97 + 165 * q^98 + 180 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(145))\)

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
145.2.a	\(\chi_{145}(1, \cdot)\)	145.2.a.a	1	1
		145.2.a.b	2
		145.2.a.c	3
		145.2.a.d	3
145.2.b	\(\chi_{145}(59, \cdot)\)	145.2.b.a	4	1
		145.2.b.b	4
		145.2.b.c	6
145.2.c	\(\chi_{145}(86, \cdot)\)	145.2.c.a	4	1
		145.2.c.b	6
145.2.d	\(\chi_{145}(144, \cdot)\)	145.2.d.a	4	1
		145.2.d.b	4
		145.2.d.c	4
145.2.e	\(\chi_{145}(12, \cdot)\)	145.2.e.a	26	2
145.2.j	\(\chi_{145}(17, \cdot)\)	145.2.j.a	26	2
145.2.k	\(\chi_{145}(16, \cdot)\)	145.2.k.a	24	6
		145.2.k.b	36
145.2.l	\(\chi_{145}(4, \cdot)\)	145.2.l.a	72	6
145.2.m	\(\chi_{145}(6, \cdot)\)	145.2.m.a	24	6
		145.2.m.b	36
145.2.n	\(\chi_{145}(24, \cdot)\)	145.2.n.a	84	6
145.2.o	\(\chi_{145}(2, \cdot)\)	145.2.o.a	156	12
145.2.t	\(\chi_{145}(3, \cdot)\)	145.2.t.a	156	12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(145))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(145)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 2}\)