Space of modular forms of level 154 and weight 2

• Label: 154.2
• Level: 154
• Weight: 2
• Dimension: 229
• Nonzero newspaces: 8
• Newform subspaces: 22
• Sturm bound: 2880
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 154 = 2 \cdot 7 \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 22 \)
Sturm bound:			\(2880\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(154))\).

	Total	New	Old
Modular forms	840	229	611
Cusp forms	601	229	372
Eisenstein series	239	0	239

Trace form

229 * q + 3 * q^2 + 8 * q^3 - q^4 + 6 * q^5 - 10 * q^6 - 11 * q^7 + 3 * q^8 - 29 * q^9 - 14 * q^10 - 9 * q^11 - 12 * q^12 + 2 * q^13 - 7 * q^14 - 36 * q^15 - q^16 - 34 * q^17 + 5 * q^18 - 14 * q^19 + 6 * q^20 - 12 * q^21 + 11 * q^22 - 16 * q^23 - 10 * q^24 - 39 * q^25 - 34 * q^26 - 58 * q^27 - 11 * q^28 - 38 * q^29 - 36 * q^30 - 20 * q^31 - 7 * q^32 - 66 * q^33 - 10 * q^34 - 54 * q^35 + q^36 - 6 * q^37 - 36 * q^38 - 60 * q^39 - 14 * q^40 - 50 * q^41 - 30 * q^42 - 72 * q^43 - 19 * q^44 - 22 * q^45 - 16 * q^46 - 8 * q^47 + 8 * q^48 - 61 * q^49 - 19 * q^50 - 34 * q^51 - 18 * q^52 - 58 * q^53 - 32 * q^54 - 74 * q^55 + 3 * q^56 - 82 * q^57 - 62 * q^58 - 58 * q^59 - 16 * q^60 - 34 * q^61 + 24 * q^62 + 71 * q^63 - q^64 + 64 * q^65 + 164 * q^66 + 16 * q^67 + 26 * q^68 + 176 * q^69 + 146 * q^70 + 152 * q^71 + 95 * q^72 + 130 * q^73 + 122 * q^74 + 354 * q^75 + 56 * q^76 + 111 * q^77 + 232 * q^78 + 144 * q^79 + 46 * q^80 + 353 * q^81 + 104 * q^82 + 146 * q^83 + 88 * q^84 + 128 * q^85 + 110 * q^86 + 196 * q^87 + 51 * q^88 + 62 * q^89 + 138 * q^90 + 102 * q^91 - 36 * q^92 + 32 * q^93 - 36 * q^94 - 40 * q^95 - 72 * q^97 - 7 * q^98 - 117 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)

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
154.2.a	\(\chi_{154}(1, \cdot)\)	154.2.a.a	1	1
		154.2.a.b	1
		154.2.a.c	1
		154.2.a.d	2
154.2.c	\(\chi_{154}(153, \cdot)\)	154.2.c.a	8	1
154.2.e	\(\chi_{154}(23, \cdot)\)	154.2.e.a	2	2
		154.2.e.b	2
		154.2.e.c	2
		154.2.e.d	2
		154.2.e.e	4
		154.2.e.f	4
154.2.f	\(\chi_{154}(15, \cdot)\)	154.2.f.a	4	4
		154.2.f.b	4
		154.2.f.c	4
		154.2.f.d	4
		154.2.f.e	8
154.2.i	\(\chi_{154}(87, \cdot)\)	154.2.i.a	16	2
154.2.k	\(\chi_{154}(13, \cdot)\)	154.2.k.a	32	4
154.2.m	\(\chi_{154}(9, \cdot)\)	154.2.m.a	8	8
		154.2.m.b	24
		154.2.m.c	32
154.2.n	\(\chi_{154}(17, \cdot)\)	154.2.n.a	64	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(154))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(154)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 2}\)