Space of modular forms of level 176 and weight 4

• Label: 176.4
• Level: 176
• Weight: 4
• Dimension: 1553
• Nonzero newspaces: 8
• Newform subspaces: 27
• Sturm bound: 7680
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 176 = 2^{4} \cdot 11 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 27 \)
Sturm bound:			\(7680\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(176))\).

	Total	New	Old
Modular forms	3020	1633	1387
Cusp forms	2740	1553	1187
Eisenstein series	280	80	200

Trace form

1553 * q - 16 * q^2 - 19 * q^3 - 36 * q^4 - 17 * q^5 + 44 * q^6 + 33 * q^7 + 68 * q^8 + 17 * q^9 + 116 * q^10 - 77 * q^11 - 240 * q^12 - 65 * q^13 - 396 * q^14 + 249 * q^15 - 580 * q^16 - 137 * q^17 - 368 * q^18 + 125 * q^19 + 372 * q^20 + 58 * q^21 + 568 * q^22 - 142 * q^23 + 1676 * q^24 + 237 * q^25 + 508 * q^26 - 79 * q^27 - 580 * q^28 - 17 * q^29 - 2492 * q^30 - 1071 * q^31 - 1956 * q^32 - 1557 * q^33 - 912 * q^34 - 1933 * q^35 + 1172 * q^36 + 339 * q^37 + 2444 * q^38 + 1189 * q^39 + 2652 * q^40 + 1871 * q^41 + 1340 * q^42 + 3060 * q^43 - 888 * q^44 + 1978 * q^45 - 2284 * q^46 + 3859 * q^47 - 3556 * q^48 - 179 * q^49 - 1472 * q^50 + 1805 * q^51 + 452 * q^52 + 275 * q^53 + 2732 * q^54 - 2597 * q^55 + 936 * q^56 - 2433 * q^57 - 36 * q^58 - 4763 * q^59 + 364 * q^60 - 2945 * q^61 + 140 * q^62 - 5664 * q^63 - 1044 * q^64 + 1022 * q^65 + 408 * q^66 - 3538 * q^67 + 1740 * q^68 - 1768 * q^69 + 6520 * q^70 + 3291 * q^71 + 13096 * q^72 + 9527 * q^73 + 10384 * q^74 + 9621 * q^75 + 9636 * q^76 + 3139 * q^77 + 2224 * q^78 + 6755 * q^79 - 1544 * q^80 - 5787 * q^81 - 10012 * q^82 + 2231 * q^83 - 21940 * q^84 - 12761 * q^85 - 21148 * q^86 - 6794 * q^87 - 29388 * q^88 - 8238 * q^89 - 29732 * q^90 - 10123 * q^91 - 12004 * q^92 - 6041 * q^93 - 4324 * q^94 - 15541 * q^95 + 5844 * q^96 + 1279 * q^97 + 4412 * q^98 - 2239 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(176))\)

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
176.4.a	\(\chi_{176}(1, \cdot)\)	176.4.a.a	1	1
		176.4.a.b	1
		176.4.a.c	1
		176.4.a.d	1
		176.4.a.e	1
		176.4.a.f	1
		176.4.a.g	2
		176.4.a.h	2
		176.4.a.i	2
		176.4.a.j	3
176.4.c	\(\chi_{176}(89, \cdot)\)	None	0	1
176.4.e	\(\chi_{176}(175, \cdot)\)	176.4.e.a	2	1
		176.4.e.b	2
		176.4.e.c	2
		176.4.e.d	4
		176.4.e.e	8
176.4.g	\(\chi_{176}(87, \cdot)\)	None	0	1
176.4.i	\(\chi_{176}(43, \cdot)\)	176.4.i.a	140	2
176.4.j	\(\chi_{176}(45, \cdot)\)	176.4.j.a	120	2
176.4.m	\(\chi_{176}(49, \cdot)\)	176.4.m.a	4	4
		176.4.m.b	8
		176.4.m.c	8
		176.4.m.d	12
		176.4.m.e	16
		176.4.m.f	20
176.4.o	\(\chi_{176}(7, \cdot)\)	None	0	4
176.4.q	\(\chi_{176}(63, \cdot)\)	176.4.q.a	24	4
		176.4.q.b	48
176.4.s	\(\chi_{176}(9, \cdot)\)	None	0	4
176.4.w	\(\chi_{176}(5, \cdot)\)	176.4.w.a	560	8
176.4.x	\(\chi_{176}(19, \cdot)\)	176.4.x.a	560	8

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(176))\) into lower level spaces

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