Space of modular forms of level 232 and weight 2

• Label: 232.2
• Level: 232
• Weight: 2
• Dimension: 889
• Nonzero newspaces: 10
• Newform subspaces: 17
• Sturm bound: 6720
• Trace bound: 6

Defining parameters

Level:	\( N \)	=	\( 232 = 2^{3} \cdot 29 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 10 \)
Newform subspaces:			\( 17 \)
Sturm bound:			\(6720\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(232))\).

	Total	New	Old
Modular forms	1848	997	851
Cusp forms	1513	889	624
Eisenstein series	335	108	227

Trace form

889 * q - 28 * q^2 - 28 * q^3 - 28 * q^4 - 28 * q^6 - 28 * q^7 - 28 * q^8 - 56 * q^9 - 28 * q^10 - 28 * q^11 - 28 * q^12 - 28 * q^14 - 28 * q^15 - 28 * q^16 - 56 * q^17 - 28 * q^18 - 28 * q^19 - 28 * q^20 - 28 * q^22 - 28 * q^23 - 28 * q^24 - 56 * q^25 - 28 * q^26 - 28 * q^27 - 28 * q^28 - 56 * q^30 - 28 * q^31 - 28 * q^32 - 56 * q^33 - 28 * q^34 - 28 * q^35 - 28 * q^36 - 28 * q^38 - 28 * q^39 - 28 * q^40 - 56 * q^41 - 28 * q^42 - 28 * q^43 - 28 * q^44 - 35 * q^45 - 28 * q^46 - 56 * q^47 - 28 * q^48 - 112 * q^49 - 28 * q^50 - 84 * q^51 - 28 * q^52 - 63 * q^53 - 28 * q^54 - 140 * q^55 - 28 * q^56 - 112 * q^57 - 28 * q^58 - 84 * q^59 - 28 * q^60 - 56 * q^61 - 28 * q^62 - 140 * q^63 - 28 * q^64 - 119 * q^65 - 28 * q^66 - 84 * q^67 - 28 * q^68 - 56 * q^69 - 28 * q^70 - 56 * q^71 - 28 * q^72 - 91 * q^73 - 28 * q^74 - 28 * q^75 - 28 * q^76 - 28 * q^78 - 28 * q^79 - 28 * q^80 - 56 * q^81 - 28 * q^82 - 28 * q^83 + 56 * q^84 - 28 * q^86 - 28 * q^87 - 56 * q^88 - 56 * q^89 - 28 * q^90 - 28 * q^91 - 28 * q^92 - 28 * q^94 - 28 * q^95 + 56 * q^96 - 35 * q^97 + 112 * q^98 + 140 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(232))\)

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
232.2.a	\(\chi_{232}(1, \cdot)\)	232.2.a.a	1	1
		232.2.a.b	1
		232.2.a.c	2
		232.2.a.d	3
232.2.c	\(\chi_{232}(117, \cdot)\)	232.2.c.a	28	1
232.2.e	\(\chi_{232}(57, \cdot)\)	232.2.e.a	8	1
232.2.g	\(\chi_{232}(173, \cdot)\)	232.2.g.a	4	1
		232.2.g.b	24
232.2.i	\(\chi_{232}(191, \cdot)\)	None	0	2
232.2.k	\(\chi_{232}(75, \cdot)\)	232.2.k.a	56	2
232.2.m	\(\chi_{232}(25, \cdot)\)	232.2.m.a	6	6
		232.2.m.b	6
		232.2.m.c	6
		232.2.m.d	24
232.2.o	\(\chi_{232}(5, \cdot)\)	232.2.o.a	168	6
232.2.q	\(\chi_{232}(9, \cdot)\)	232.2.q.a	48	6
232.2.s	\(\chi_{232}(45, \cdot)\)	232.2.s.a	168	6
232.2.v	\(\chi_{232}(3, \cdot)\)	232.2.v.a	336	12
232.2.x	\(\chi_{232}(15, \cdot)\)	None	0	12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(232))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(232)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 2}\)