Space of modular forms of level 148 and weight 2

• Label: 148.2
• Level: 148
• Weight: 2
• Dimension: 363
• Nonzero newspaces: 9
• Newform subspaces: 16
• Sturm bound: 2736
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 148 = 2^{2} \cdot 37 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 9 \)
Newform subspaces:			\( 16 \)
Sturm bound:			\(2736\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(148))\).

	Total	New	Old
Modular forms	774	435	339
Cusp forms	595	363	232
Eisenstein series	179	72	107

Trace form

363 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 18 * q^26 - 24 * q^27 - 18 * q^28 - 54 * q^29 - 18 * q^30 - 54 * q^31 - 18 * q^32 - 72 * q^33 - 18 * q^34 - 54 * q^35 - 78 * q^37 - 36 * q^38 - 42 * q^39 - 18 * q^40 - 90 * q^41 - 18 * q^42 - 36 * q^43 - 18 * q^44 - 90 * q^45 - 18 * q^46 - 18 * q^47 - 18 * q^48 - 60 * q^49 - 18 * q^50 - 18 * q^52 - 36 * q^53 - 18 * q^54 - 18 * q^56 - 36 * q^57 + 36 * q^59 + 108 * q^60 + 9 * q^61 + 72 * q^62 + 108 * q^63 + 108 * q^64 + 45 * q^65 + 234 * q^66 + 36 * q^67 + 90 * q^68 + 108 * q^69 + 180 * q^70 + 72 * q^71 + 234 * q^72 + 72 * q^73 + 126 * q^74 + 180 * q^75 + 126 * q^76 + 36 * q^77 + 234 * q^78 + 72 * q^79 + 180 * q^80 + 108 * q^81 + 90 * q^82 + 36 * q^83 + 234 * q^84 + 45 * q^85 + 108 * q^86 + 108 * q^87 + 72 * q^88 + 9 * q^89 + 108 * q^90 + 30 * q^91 - 90 * q^93 - 18 * q^94 - 72 * q^95 - 18 * q^96 - 108 * q^97 - 18 * q^98 - 90 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(148))\)

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
148.2.a	\(\chi_{148}(1, \cdot)\)	148.2.a.a	1	1
		148.2.a.b	2
148.2.d	\(\chi_{148}(73, \cdot)\)	148.2.d.a	2	1
148.2.e	\(\chi_{148}(121, \cdot)\)	148.2.e.a	6	2
148.2.g	\(\chi_{148}(31, \cdot)\)	148.2.g.a	2	2
		148.2.g.b	4
		148.2.g.c	28
148.2.h	\(\chi_{148}(85, \cdot)\)	148.2.h.a	2	2
		148.2.h.b	2
148.2.k	\(\chi_{148}(9, \cdot)\)	148.2.k.a	24	6
148.2.l	\(\chi_{148}(23, \cdot)\)	148.2.l.a	4	4
		148.2.l.b	64
148.2.n	\(\chi_{148}(21, \cdot)\)	148.2.n.a	6	6
		148.2.n.b	12
148.2.q	\(\chi_{148}(15, \cdot)\)	148.2.q.a	12	12
		148.2.q.b	192

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(148))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(148)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 2}\)