Space of modular forms of level 176 and weight 6

• Label: 176.6
• Level: 176
• Weight: 6
• Dimension: 2615
• Nonzero newspaces: 8
• Sturm bound: 11520
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 176 = 2^{4} \cdot 11 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(11520\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(176))\).

	Total	New	Old
Modular forms	4940	2695	2245
Cusp forms	4660	2615	2045
Eisenstein series	280	80	200

Trace form

2615 * q - 16 * q^2 + 5 * q^3 + 28 * q^4 + 19 * q^5 - 244 * q^6 - 239 * q^7 - 508 * q^8 - 121 * q^9 + 852 * q^10 + 1255 * q^11 - 48 * q^12 - 141 * q^13 + 180 * q^14 - 7863 * q^15 + 1724 * q^16 + 1171 * q^17 + 6256 * q^18 + 12469 * q^19 - 5964 * q^20 - 2150 * q^21 - 4440 * q^22 - 7870 * q^23 - 16756 * q^24 - 4289 * q^25 - 14756 * q^26 - 3679 * q^27 + 14652 * q^28 - 413 * q^29 + 60868 * q^30 + 20113 * q^31 + 47964 * q^32 - 19821 * q^33 + 3440 * q^34 + 18731 * q^35 - 13804 * q^36 + 27839 * q^37 - 106516 * q^38 + 34837 * q^39 - 150564 * q^40 - 64885 * q^41 - 66820 * q^42 - 67292 * q^43 + 40104 * q^44 - 67706 * q^45 + 185044 * q^46 - 49901 * q^47 + 295964 * q^48 + 143163 * q^49 + 170080 * q^50 + 129005 * q^51 - 183164 * q^52 - 50017 * q^53 - 417364 * q^54 + 19939 * q^55 - 382296 * q^56 - 264681 * q^57 - 213572 * q^58 + 77869 * q^59 + 308716 * q^60 + 202579 * q^61 + 547724 * q^62 + 35400 * q^63 + 567532 * q^64 + 60470 * q^65 + 153336 * q^66 + 162950 * q^67 - 267444 * q^68 - 152704 * q^69 - 488200 * q^70 + 2811 * q^71 - 219608 * q^72 - 59677 * q^73 - 642416 * q^74 - 451971 * q^75 - 972444 * q^76 - 564269 * q^77 - 250640 * q^78 - 200541 * q^79 + 457912 * q^80 + 114771 * q^81 + 426212 * q^82 - 27481 * q^83 + 786764 * q^84 + 1031183 * q^85 + 201284 * q^86 + 337126 * q^87 + 1803572 * q^88 + 346014 * q^89 + 1279996 * q^90 + 763077 * q^91 + 794012 * q^92 - 45977 * q^93 + 302364 * q^94 - 115429 * q^95 - 315564 * q^96 - 1015893 * q^97 - 1603108 * q^98 - 348787 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(176))\)

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
176.6.a	\(\chi_{176}(1, \cdot)\)	176.6.a.a	1	1
		176.6.a.b	1
		176.6.a.c	1
		176.6.a.d	1
		176.6.a.e	1
		176.6.a.f	2
		176.6.a.g	2
		176.6.a.h	2
		176.6.a.i	3
		176.6.a.j	3
		176.6.a.k	4
		176.6.a.l	4
176.6.c	\(\chi_{176}(89, \cdot)\)	None	0	1
176.6.e	\(\chi_{176}(175, \cdot)\)	176.6.e.a	2	1
		176.6.e.b	4
		176.6.e.c	8
		176.6.e.d	16
176.6.g	\(\chi_{176}(87, \cdot)\)	None	0	1
176.6.i	\(\chi_{176}(43, \cdot)\)	n/a	236	2
176.6.j	\(\chi_{176}(45, \cdot)\)	n/a	200	2
176.6.m	\(\chi_{176}(49, \cdot)\)	n/a	116	4
176.6.o	\(\chi_{176}(7, \cdot)\)	None	0	4
176.6.q	\(\chi_{176}(63, \cdot)\)	n/a	120	4
176.6.s	\(\chi_{176}(9, \cdot)\)	None	0	4
176.6.w	\(\chi_{176}(5, \cdot)\)	n/a	944	8
176.6.x	\(\chi_{176}(19, \cdot)\)	n/a	944	8

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(176))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(176)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 1}\)