Space of modular forms of level 153 and weight 4

• Label: 153.4
• Level: 153
• Weight: 4
• Dimension: 1970
• Nonzero newspaces: 10
• Newform subspaces: 27
• Sturm bound: 6912
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 10 \)
Newform subspaces:			\( 27 \)
Sturm bound:			\(6912\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(153))\).

	Total	New	Old
Modular forms	2720	2104	616
Cusp forms	2464	1970	494
Eisenstein series	256	134	122

Trace form

1970 * q - 18 * q^2 - 26 * q^3 + 2 * q^4 + 6 * q^5 - 50 * q^6 - 50 * q^7 - 156 * q^8 - 122 * q^9 - 200 * q^10 - 4 * q^11 + 280 * q^12 + 126 * q^13 + 256 * q^14 - 86 * q^15 + 274 * q^16 - 94 * q^17 - 496 * q^18 + 204 * q^19 + 64 * q^20 - 74 * q^21 - 314 * q^22 - 166 * q^23 + 166 * q^24 - 1244 * q^25 + 832 * q^27 - 272 * q^28 + 134 * q^29 - 608 * q^30 + 310 * q^31 + 562 * q^32 - 428 * q^33 + 2385 * q^34 + 932 * q^35 + 418 * q^36 + 580 * q^37 + 1918 * q^38 + 1074 * q^39 + 5688 * q^40 + 2660 * q^41 + 3052 * q^42 + 112 * q^43 - 3100 * q^44 + 38 * q^45 - 3864 * q^46 - 3786 * q^47 - 7030 * q^48 - 5772 * q^49 - 9258 * q^50 - 3529 * q^51 - 11924 * q^52 - 6180 * q^53 - 6718 * q^54 - 8308 * q^55 - 7292 * q^56 + 1770 * q^57 - 856 * q^58 + 3524 * q^59 + 5160 * q^60 + 4570 * q^61 + 13400 * q^62 + 3850 * q^63 + 18660 * q^64 + 11646 * q^65 + 5116 * q^66 + 5848 * q^67 + 4309 * q^68 - 1846 * q^69 + 1884 * q^70 - 5304 * q^71 - 790 * q^72 - 332 * q^73 + 1872 * q^74 + 694 * q^75 - 1698 * q^76 - 562 * q^77 + 1948 * q^78 - 3750 * q^79 + 2728 * q^80 + 1102 * q^81 - 7748 * q^82 + 3818 * q^83 + 15084 * q^84 + 18150 * q^85 + 36002 * q^86 + 10738 * q^87 + 24882 * q^88 + 11016 * q^89 + 8920 * q^90 + 9596 * q^91 - 3196 * q^92 - 3318 * q^93 - 9168 * q^94 - 15280 * q^95 - 23776 * q^96 - 5972 * q^97 - 38172 * q^98 - 14306 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(153))\)

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
153.4.a	\(\chi_{153}(1, \cdot)\)	153.4.a.a	1	1
		153.4.a.b	1
		153.4.a.c	1
		153.4.a.d	1
		153.4.a.e	2
		153.4.a.f	3
		153.4.a.g	3
		153.4.a.h	4
		153.4.a.i	4
153.4.d	\(\chi_{153}(118, \cdot)\)	153.4.d.a	2	1
		153.4.d.b	4
		153.4.d.c	8
		153.4.d.d	8
153.4.e	\(\chi_{153}(52, \cdot)\)	153.4.e.a	44	2
		153.4.e.b	52
153.4.f	\(\chi_{153}(55, \cdot)\)	153.4.f.a	8	2
		153.4.f.b	16
		153.4.f.c	20
153.4.h	\(\chi_{153}(16, \cdot)\)	153.4.h.a	104	2
153.4.l	\(\chi_{153}(19, \cdot)\)	153.4.l.a	12	4
		153.4.l.b	32
		153.4.l.c	40
153.4.n	\(\chi_{153}(4, \cdot)\)	153.4.n.a	208	4
153.4.o	\(\chi_{153}(44, \cdot)\)	153.4.o.a	72	8
		153.4.o.b	72
153.4.r	\(\chi_{153}(25, \cdot)\)	153.4.r.a	416	8
153.4.s	\(\chi_{153}(5, \cdot)\)	153.4.s.a	832	16

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(153))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(153)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 2}\)