Space of modular forms of level 261 and weight 2

• Label: 261.2
• Level: 261
• Weight: 2
• Dimension: 1869
• Nonzero newspaces: 12
• Newform subspaces: 26
• Sturm bound: 10080
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 26 \)
Sturm bound:			\(10080\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(261))\).

	Total	New	Old
Modular forms	2744	2111	633
Cusp forms	2297	1869	428
Eisenstein series	447	242	205

Trace form

1869 * q - 42 * q^2 - 56 * q^3 - 42 * q^4 - 42 * q^5 - 56 * q^6 - 42 * q^7 - 42 * q^8 - 56 * q^9 - 126 * q^10 - 42 * q^11 - 56 * q^12 - 42 * q^13 - 42 * q^14 - 56 * q^15 - 42 * q^16 - 42 * q^17 - 56 * q^18 - 126 * q^19 - 63 * q^20 - 56 * q^21 - 70 * q^22 - 56 * q^23 - 56 * q^24 - 70 * q^25 - 77 * q^26 - 56 * q^27 - 196 * q^28 - 70 * q^29 - 112 * q^30 - 70 * q^31 - 98 * q^32 - 56 * q^33 - 77 * q^34 - 70 * q^35 - 56 * q^36 - 140 * q^37 - 70 * q^38 - 56 * q^39 - 63 * q^40 - 42 * q^41 - 56 * q^42 - 42 * q^43 - 56 * q^44 - 56 * q^45 - 196 * q^46 - 70 * q^47 - 56 * q^48 - 98 * q^49 - 140 * q^50 - 56 * q^51 - 154 * q^52 - 105 * q^53 - 56 * q^54 - 238 * q^55 - 56 * q^56 - 56 * q^57 - 210 * q^58 - 112 * q^59 - 56 * q^60 - 98 * q^61 - 140 * q^62 - 56 * q^63 - 252 * q^64 - 105 * q^65 - 56 * q^66 - 98 * q^67 - 140 * q^68 - 56 * q^69 - 70 * q^70 + 56 * q^71 + 112 * q^72 - 77 * q^73 + 196 * q^74 + 84 * q^75 + 294 * q^76 + 168 * q^77 + 168 * q^78 + 42 * q^79 + 546 * q^80 + 168 * q^81 + 42 * q^82 + 126 * q^83 + 280 * q^84 + 210 * q^85 + 420 * q^86 + 84 * q^87 + 420 * q^88 + 168 * q^89 + 224 * q^90 + 126 * q^91 + 462 * q^92 + 56 * q^93 + 126 * q^94 + 294 * q^95 + 336 * q^96 - 7 * q^97 + 224 * q^98 + 84 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(261))\)

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
261.2.a	\(\chi_{261}(1, \cdot)\)	261.2.a.a	2	1
		261.2.a.b	2
		261.2.a.c	2
		261.2.a.d	2
		261.2.a.e	3
261.2.c	\(\chi_{261}(28, \cdot)\)	261.2.c.a	2	1
		261.2.c.b	4
		261.2.c.c	6
261.2.e	\(\chi_{261}(88, \cdot)\)	261.2.e.a	22	2
		261.2.e.b	34
261.2.g	\(\chi_{261}(17, \cdot)\)	261.2.g.a	4	2
		261.2.g.b	8
		261.2.g.c	8
261.2.i	\(\chi_{261}(115, \cdot)\)	261.2.i.a	56	2
261.2.k	\(\chi_{261}(82, \cdot)\)	261.2.k.a	6	6
		261.2.k.b	18
		261.2.k.c	18
		261.2.k.d	24
261.2.l	\(\chi_{261}(41, \cdot)\)	261.2.l.a	112	4
261.2.o	\(\chi_{261}(64, \cdot)\)	261.2.o.a	12	6
		261.2.o.b	24
		261.2.o.c	36
261.2.q	\(\chi_{261}(7, \cdot)\)	261.2.q.a	336	12
261.2.r	\(\chi_{261}(8, \cdot)\)	261.2.r.a	120	12
261.2.u	\(\chi_{261}(4, \cdot)\)	261.2.u.a	336	12
261.2.x	\(\chi_{261}(2, \cdot)\)	261.2.x.a	672	24

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(261))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(261)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 2}\)