Space of modular forms of level 231 and weight 2

• Label: 231.2
• Level: 231
• Weight: 2
• Dimension: 1271
• Nonzero newspaces: 16
• Newform subspaces: 33
• Sturm bound: 7680
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Newform subspaces:			\( 33 \)
Sturm bound:			\(7680\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(231))\).

	Total	New	Old
Modular forms	2160	1447	713
Cusp forms	1681	1271	410
Eisenstein series	479	176	303

Trace form

1271 * q + 9 * q^2 - 13 * q^3 - 23 * q^4 + 6 * q^5 - 33 * q^6 - 49 * q^7 - 31 * q^8 - 45 * q^9 - 94 * q^10 - 15 * q^11 - 79 * q^12 - 46 * q^13 - 33 * q^14 - 72 * q^15 - 127 * q^16 - 30 * q^17 - 41 * q^18 - 68 * q^19 - 46 * q^20 - 43 * q^21 - 175 * q^22 - 16 * q^23 - 61 * q^24 - 99 * q^25 - 58 * q^26 + 5 * q^27 - 127 * q^28 - 22 * q^29 - 24 * q^30 - 60 * q^31 + 17 * q^32 + 5 * q^33 - 118 * q^34 - 34 * q^35 - 35 * q^36 - 86 * q^37 - 28 * q^38 - 56 * q^39 - 158 * q^40 - 42 * q^41 - 39 * q^42 - 188 * q^43 - 143 * q^44 - 124 * q^45 - 228 * q^46 - 104 * q^47 - 121 * q^48 - 157 * q^49 - 121 * q^50 - 100 * q^51 - 190 * q^52 - 74 * q^53 - 41 * q^54 - 134 * q^55 - 99 * q^56 - 68 * q^57 - 118 * q^58 - 48 * q^59 + 140 * q^60 - 18 * q^61 + 24 * q^62 + 51 * q^63 + 53 * q^64 + 132 * q^65 + 263 * q^66 + 12 * q^67 + 274 * q^68 + 134 * q^69 + 214 * q^70 + 216 * q^71 + 359 * q^72 + 94 * q^73 + 198 * q^74 + 191 * q^75 + 380 * q^76 + 113 * q^77 + 70 * q^78 - 36 * q^79 + 378 * q^80 + 219 * q^81 + 70 * q^82 + 4 * q^83 + 283 * q^84 - 36 * q^85 + 224 * q^86 + 42 * q^87 + 153 * q^88 + 110 * q^89 + 120 * q^90 + 22 * q^91 + 68 * q^92 - 10 * q^93 - 100 * q^94 - 108 * q^95 + 147 * q^96 - 194 * q^97 - 223 * q^98 - 99 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(231))\)

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
231.2.a	\(\chi_{231}(1, \cdot)\)	231.2.a.a	1	1
		231.2.a.b	2
		231.2.a.c	2
		231.2.a.d	3
		231.2.a.e	3
231.2.c	\(\chi_{231}(76, \cdot)\)	231.2.c.a	16	1
231.2.e	\(\chi_{231}(188, \cdot)\)	231.2.e.a	28	1
231.2.g	\(\chi_{231}(197, \cdot)\)	231.2.g.a	24	1
231.2.i	\(\chi_{231}(67, \cdot)\)	231.2.i.a	2	2
		231.2.i.b	2
		231.2.i.c	2
		231.2.i.d	4
		231.2.i.e	8
		231.2.i.f	10
231.2.j	\(\chi_{231}(64, \cdot)\)	231.2.j.a	4	4
		231.2.j.b	4
		231.2.j.c	4
		231.2.j.d	4
		231.2.j.e	4
		231.2.j.f	8
		231.2.j.g	20
231.2.l	\(\chi_{231}(32, \cdot)\)	231.2.l.a	8	2
		231.2.l.b	48
231.2.n	\(\chi_{231}(89, \cdot)\)	231.2.n.a	52	2
231.2.p	\(\chi_{231}(10, \cdot)\)	231.2.p.a	32	2
231.2.s	\(\chi_{231}(8, \cdot)\)	231.2.s.a	96	4
231.2.u	\(\chi_{231}(20, \cdot)\)	231.2.u.a	112	4
231.2.w	\(\chi_{231}(13, \cdot)\)	231.2.w.a	64	4
231.2.y	\(\chi_{231}(4, \cdot)\)	231.2.y.a	64	8
		231.2.y.b	64
231.2.ba	\(\chi_{231}(19, \cdot)\)	231.2.ba.a	128	8
231.2.bc	\(\chi_{231}(5, \cdot)\)	231.2.bc.a	224	8
231.2.be	\(\chi_{231}(2, \cdot)\)	231.2.be.a	224	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(231))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(231)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 2}\)