Space of modular forms of level 176 and weight 2

• Label: 176.2
• Level: 176
• Weight: 2
• Dimension: 491
• Nonzero newspaces: 8
• Newform subspaces: 16
• Sturm bound: 3840
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 176 = 2^{4} \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 16 \)
Sturm bound:			\(3840\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(176))\).

	Total	New	Old
Modular forms	1100	571	529
Cusp forms	821	491	330
Eisenstein series	279	80	199

Trace form

491 * q - 16 * q^2 - 11 * q^3 - 20 * q^4 - 21 * q^5 - 28 * q^6 - 15 * q^7 - 28 * q^8 - 5 * q^9 - 20 * q^10 - 17 * q^11 - 32 * q^12 - 21 * q^13 - 12 * q^14 - 23 * q^15 - 4 * q^16 - 37 * q^17 - 24 * q^18 - 27 * q^19 - 28 * q^20 - 38 * q^21 - 20 * q^22 - 30 * q^23 - 20 * q^24 - 5 * q^25 - 28 * q^26 + q^27 - 36 * q^28 - 37 * q^29 - 12 * q^30 + 17 * q^31 - 36 * q^32 - 61 * q^33 - 48 * q^34 - 37 * q^35 - 12 * q^36 - 57 * q^37 + 4 * q^38 - 75 * q^39 - 4 * q^40 - 45 * q^41 - 20 * q^42 - 60 * q^43 - 16 * q^44 - 114 * q^45 - 44 * q^46 - 77 * q^47 - 36 * q^48 - 97 * q^49 - 8 * q^50 - 83 * q^51 - 12 * q^52 - 25 * q^53 - 20 * q^54 - 45 * q^55 - 24 * q^56 - 25 * q^57 + 4 * q^58 - 3 * q^59 - 20 * q^60 + 11 * q^61 - 52 * q^62 - 8 * q^63 - 20 * q^64 - 58 * q^65 - 24 * q^66 - 10 * q^67 - 20 * q^68 - 16 * q^69 + 104 * q^70 - 5 * q^71 + 72 * q^72 + 75 * q^73 + 80 * q^74 + 13 * q^75 + 116 * q^76 + 51 * q^77 + 208 * q^78 + 35 * q^79 + 184 * q^80 + 55 * q^81 + 180 * q^82 + 39 * q^83 + 236 * q^84 + 127 * q^85 + 140 * q^86 + 70 * q^87 + 292 * q^88 + 70 * q^89 + 308 * q^90 + 37 * q^91 + 188 * q^92 + 103 * q^93 + 252 * q^94 + 59 * q^95 + 212 * q^96 + 83 * q^97 + 212 * q^98 + 37 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)

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
176.2.a	\(\chi_{176}(1, \cdot)\)	176.2.a.a	1	1
		176.2.a.b	1
		176.2.a.c	1
		176.2.a.d	2
176.2.c	\(\chi_{176}(89, \cdot)\)	None	0	1
176.2.e	\(\chi_{176}(175, \cdot)\)	176.2.e.a	2	1
		176.2.e.b	4
176.2.g	\(\chi_{176}(87, \cdot)\)	None	0	1
176.2.i	\(\chi_{176}(43, \cdot)\)	176.2.i.a	44	2
176.2.j	\(\chi_{176}(45, \cdot)\)	176.2.j.a	40	2
176.2.m	\(\chi_{176}(49, \cdot)\)	176.2.m.a	4	4
		176.2.m.b	4
		176.2.m.c	4
		176.2.m.d	8
176.2.o	\(\chi_{176}(7, \cdot)\)	None	0	4
176.2.q	\(\chi_{176}(63, \cdot)\)	176.2.q.a	8	4
		176.2.q.b	16
176.2.s	\(\chi_{176}(9, \cdot)\)	None	0	4
176.2.w	\(\chi_{176}(5, \cdot)\)	176.2.w.a	176	8
176.2.x	\(\chi_{176}(19, \cdot)\)	176.2.x.a	176	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(176))\) into lower level spaces

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