Space of modular forms of level 605 and weight 2

• Label: 605.2
• Level: 605
• Weight: 2
• Dimension: 12671
• Nonzero newspaces: 12
• Newform subspaces: 67
• Sturm bound: 58080
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 67 \)
Sturm bound:			\(58080\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(605))\).

	Total	New	Old
Modular forms	15160	13513	1647
Cusp forms	13881	12671	1210
Eisenstein series	1279	842	437

Trace form

12671 * q - 87 * q^2 - 86 * q^3 - 83 * q^4 - 134 * q^5 - 278 * q^6 - 102 * q^7 - 115 * q^8 - 117 * q^9 - 162 * q^10 - 310 * q^11 - 222 * q^12 - 96 * q^13 - 126 * q^14 - 171 * q^15 - 359 * q^16 - 132 * q^17 - 171 * q^18 - 130 * q^19 - 198 * q^20 - 338 * q^21 - 160 * q^22 - 206 * q^23 - 250 * q^24 - 194 * q^25 - 408 * q^26 - 170 * q^27 - 254 * q^28 - 160 * q^29 - 253 * q^30 - 318 * q^31 - 227 * q^32 - 180 * q^33 - 276 * q^34 - 217 * q^35 - 539 * q^36 - 172 * q^37 - 250 * q^38 - 254 * q^39 - 130 * q^40 - 408 * q^41 - 294 * q^42 - 146 * q^43 - 160 * q^44 - 262 * q^45 - 298 * q^46 - 62 * q^47 - 106 * q^48 - 53 * q^49 - 82 * q^50 - 298 * q^51 - 12 * q^52 - 136 * q^53 - 110 * q^54 - 130 * q^55 - 510 * q^56 - 150 * q^57 - 20 * q^58 - 110 * q^59 - 117 * q^60 - 228 * q^61 - 254 * q^62 - 166 * q^63 - 163 * q^64 - 151 * q^65 - 470 * q^66 - 242 * q^67 - 304 * q^68 - 274 * q^69 - 301 * q^70 - 478 * q^71 - 415 * q^72 - 276 * q^73 - 436 * q^74 - 311 * q^75 - 670 * q^76 - 270 * q^77 - 602 * q^78 - 350 * q^79 - 474 * q^80 - 609 * q^81 - 384 * q^82 - 346 * q^83 - 566 * q^84 - 327 * q^85 - 598 * q^86 - 430 * q^87 - 420 * q^88 - 340 * q^89 - 186 * q^90 - 538 * q^91 - 382 * q^92 - 242 * q^93 - 286 * q^94 - 185 * q^95 - 478 * q^96 - 152 * q^97 - 119 * q^98 - 180 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(605))\)

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
605.2.a	\(\chi_{605}(1, \cdot)\)	605.2.a.a	1	1
		605.2.a.b	1
		605.2.a.c	1
		605.2.a.d	2
		605.2.a.e	2
		605.2.a.f	2
		605.2.a.g	3
		605.2.a.h	3
		605.2.a.i	4
		605.2.a.j	4
		605.2.a.k	4
		605.2.a.l	4
		605.2.a.m	6
605.2.b	\(\chi_{605}(364, \cdot)\)	605.2.b.a	2	1
		605.2.b.b	4
		605.2.b.c	4
		605.2.b.d	4
		605.2.b.e	4
		605.2.b.f	8
		605.2.b.g	8
		605.2.b.h	12
605.2.e	\(\chi_{605}(362, \cdot)\)	605.2.e.a	20	2
		605.2.e.b	32
		605.2.e.c	40
605.2.g	\(\chi_{605}(81, \cdot)\)	605.2.g.a	4	4
		605.2.g.b	4
		605.2.g.c	4
		605.2.g.d	4
		605.2.g.e	8
		605.2.g.f	8
		605.2.g.g	8
		605.2.g.h	8
		605.2.g.i	8
		605.2.g.j	8
		605.2.g.k	8
		605.2.g.l	8
		605.2.g.m	8
		605.2.g.n	8
		605.2.g.o	12
		605.2.g.p	12
		605.2.g.q	24
605.2.j	\(\chi_{605}(9, \cdot)\)	605.2.j.a	8	4
		605.2.j.b	8
		605.2.j.c	8
		605.2.j.d	16
		605.2.j.e	16
		605.2.j.f	16
		605.2.j.g	16
		605.2.j.h	16
		605.2.j.i	16
		605.2.j.j	16
		605.2.j.k	48
605.2.k	\(\chi_{605}(56, \cdot)\)	605.2.k.a	220	10
		605.2.k.b	220
605.2.m	\(\chi_{605}(112, \cdot)\)	605.2.m.a	16	8
		605.2.m.b	16
		605.2.m.c	32
		605.2.m.d	32
		605.2.m.e	32
		605.2.m.f	80
		605.2.m.g	160
605.2.o	\(\chi_{605}(34, \cdot)\)	605.2.o.a	640	10
605.2.r	\(\chi_{605}(32, \cdot)\)	605.2.r.a	1280	20
605.2.s	\(\chi_{605}(16, \cdot)\)	605.2.s.a	880	40
		605.2.s.b	880
605.2.u	\(\chi_{605}(4, \cdot)\)	605.2.u.a	2560	40
605.2.w	\(\chi_{605}(2, \cdot)\)	605.2.w.a	5120	80

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(605))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(605)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 2}\)