Space of modular forms of level 605 and weight 4

• Label: 605.4
• Level: 605
• Weight: 4
• Dimension: 38851
• Nonzero newspaces: 12
• Sturm bound: 116160
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(116160\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(605))\).

	Total	New	Old
Modular forms	44200	39693	4507
Cusp forms	42920	38851	4069
Eisenstein series	1280	842	438

Trace form

38851 * q - 94 * q^2 - 88 * q^3 - 82 * q^4 - 140 * q^5 - 478 * q^6 - 124 * q^7 + 70 * q^8 + 207 * q^9 + 75 * q^10 - 200 * q^11 + 486 * q^12 - 48 * q^13 - 894 * q^14 - 765 * q^15 - 1854 * q^16 - 664 * q^17 - 18 * q^18 + 910 * q^19 + 695 * q^20 + 1402 * q^21 + 1160 * q^22 - 648 * q^23 - 850 * q^24 - 230 * q^25 - 818 * q^26 - 610 * q^27 - 702 * q^28 - 340 * q^29 - 845 * q^30 - 1938 * q^31 + 1066 * q^32 - 510 * q^33 - 1634 * q^34 - 25 * q^35 - 274 * q^36 + 736 * q^37 + 1050 * q^38 + 2914 * q^39 + 2515 * q^40 + 1792 * q^41 + 8162 * q^42 + 3772 * q^43 + 2150 * q^44 + 5960 * q^45 + 6502 * q^46 + 1996 * q^47 + 1642 * q^48 - 1237 * q^49 - 4245 * q^50 - 8558 * q^51 - 20334 * q^52 - 14248 * q^53 - 29750 * q^54 - 6070 * q^55 - 22870 * q^56 - 13190 * q^57 - 8510 * q^58 + 1590 * q^59 - 4485 * q^60 - 1428 * q^61 + 11042 * q^62 + 4112 * q^63 + 13718 * q^64 + 8605 * q^65 + 8550 * q^66 + 15596 * q^67 + 26018 * q^68 + 15934 * q^69 + 15155 * q^70 + 2022 * q^71 + 9270 * q^72 - 11168 * q^73 - 7014 * q^74 - 185 * q^75 + 1310 * q^76 - 4560 * q^77 - 6946 * q^78 - 1650 * q^79 - 6725 * q^80 - 5109 * q^81 - 12098 * q^82 + 2292 * q^83 - 694 * q^84 + 5415 * q^85 + 1602 * q^86 + 13870 * q^87 + 9260 * q^88 + 7480 * q^89 + 28275 * q^90 + 23822 * q^91 + 28746 * q^92 + 27974 * q^93 + 37506 * q^94 + 18805 * q^95 + 42342 * q^96 + 14996 * q^97 + 18758 * q^98 + 3340 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(605))\)

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
605.4.a	\(\chi_{605}(1, \cdot)\)	605.4.a.a	1	1
		605.4.a.b	1
		605.4.a.c	1
		605.4.a.d	1
		605.4.a.e	2
		605.4.a.f	2
		605.4.a.g	2
		605.4.a.h	3
		605.4.a.i	4
		605.4.a.j	4
		605.4.a.k	4
		605.4.a.l	4
		605.4.a.m	6
		605.4.a.n	6
		605.4.a.o	8
		605.4.a.p	12
		605.4.a.q	12
		605.4.a.r	12
		605.4.a.s	12
		605.4.a.t	12
605.4.b	\(\chi_{605}(364, \cdot)\)	n/a	154	1
605.4.e	\(\chi_{605}(362, \cdot)\)	n/a	308	2
605.4.g	\(\chi_{605}(81, \cdot)\)	n/a	432	4
605.4.j	\(\chi_{605}(9, \cdot)\)	n/a	616	4
605.4.k	\(\chi_{605}(56, \cdot)\)	n/a	1320	10
605.4.m	\(\chi_{605}(112, \cdot)\)	n/a	1232	8
605.4.o	\(\chi_{605}(34, \cdot)\)	n/a	1960	10
605.4.r	\(\chi_{605}(32, \cdot)\)	n/a	3920	20
605.4.s	\(\chi_{605}(16, \cdot)\)	n/a	5280	40
605.4.u	\(\chi_{605}(4, \cdot)\)	n/a	7840	40
605.4.w	\(\chi_{605}(2, \cdot)\)	n/a	15680	80

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(605))\) into lower level spaces

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