Space of modular forms of level 296 and weight 2

• Label: 296.2
• Level: 296
• Weight: 2
• Dimension: 1467
• Nonzero newspaces: 15
• Newform subspaces: 26
• Sturm bound: 10944
• Trace bound: 6

Defining parameters

Level:	\( N \)	=	\( 296 = 2^{3} \cdot 37 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 15 \)
Newform subspaces:			\( 26 \)
Sturm bound:			\(10944\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(296))\).

	Total	New	Old
Modular forms	2952	1607	1345
Cusp forms	2521	1467	1054
Eisenstein series	431	140	291

Trace form

1467 * q - 36 * q^2 - 36 * q^3 - 36 * q^4 - 36 * q^6 - 36 * q^7 - 36 * q^8 - 72 * q^9 - 36 * q^10 - 36 * q^11 - 36 * q^12 - 36 * q^14 - 36 * q^15 - 36 * q^16 - 72 * q^17 - 36 * q^18 - 36 * q^19 - 36 * q^20 - 36 * q^22 - 36 * q^23 - 36 * q^24 - 72 * q^25 - 36 * q^26 - 36 * q^27 - 36 * q^28 - 36 * q^30 - 36 * q^31 - 36 * q^32 - 72 * q^33 - 36 * q^34 - 36 * q^35 - 36 * q^36 - 72 * q^38 - 36 * q^39 - 36 * q^40 - 72 * q^41 - 36 * q^42 - 36 * q^43 - 36 * q^44 - 36 * q^46 - 36 * q^47 - 36 * q^48 - 72 * q^49 - 36 * q^50 - 36 * q^51 - 36 * q^52 - 36 * q^54 - 36 * q^55 - 36 * q^56 - 72 * q^57 - 36 * q^58 - 72 * q^59 - 36 * q^60 - 45 * q^61 - 36 * q^62 - 144 * q^63 - 36 * q^64 - 153 * q^65 - 36 * q^66 - 72 * q^67 - 36 * q^68 - 144 * q^69 - 36 * q^70 - 108 * q^71 - 36 * q^72 - 144 * q^73 - 36 * q^74 - 252 * q^75 - 36 * q^76 - 72 * q^77 - 36 * q^78 - 108 * q^79 - 36 * q^80 - 216 * q^81 - 36 * q^82 - 72 * q^83 - 36 * q^84 - 81 * q^85 - 36 * q^86 - 144 * q^87 - 36 * q^88 - 117 * q^89 - 36 * q^90 - 72 * q^91 - 36 * q^92 - 36 * q^94 - 36 * q^95 - 36 * q^96 - 72 * q^97 - 36 * q^98 - 36 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(296))\)

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
296.2.a	\(\chi_{296}(1, \cdot)\)	296.2.a.a	1	1
		296.2.a.b	1
		296.2.a.c	3
		296.2.a.d	4
296.2.c	\(\chi_{296}(149, \cdot)\)	296.2.c.a	4	1
		296.2.c.b	4
		296.2.c.c	28
296.2.e	\(\chi_{296}(221, \cdot)\)	296.2.e.a	36	1
296.2.g	\(\chi_{296}(73, \cdot)\)	296.2.g.a	10	1
296.2.i	\(\chi_{296}(121, \cdot)\)	296.2.i.a	2	2
		296.2.i.b	6
		296.2.i.c	10
296.2.j	\(\chi_{296}(43, \cdot)\)	296.2.j.a	8	2
		296.2.j.b	64
296.2.l	\(\chi_{296}(31, \cdot)\)	None	0	2
296.2.o	\(\chi_{296}(233, \cdot)\)	296.2.o.a	20	2
296.2.q	\(\chi_{296}(85, \cdot)\)	296.2.q.a	72	2
296.2.s	\(\chi_{296}(269, \cdot)\)	296.2.s.a	72	2
296.2.u	\(\chi_{296}(9, \cdot)\)	296.2.u.a	24	6
		296.2.u.b	30
296.2.w	\(\chi_{296}(23, \cdot)\)	None	0	4
296.2.y	\(\chi_{296}(51, \cdot)\)	296.2.y.a	4	4
		296.2.y.b	4
		296.2.y.c	136
296.2.ba	\(\chi_{296}(25, \cdot)\)	296.2.ba.a	60	6
296.2.bc	\(\chi_{296}(53, \cdot)\)	296.2.bc.a	216	6
296.2.bf	\(\chi_{296}(21, \cdot)\)	296.2.bf.a	216	6
296.2.bh	\(\chi_{296}(15, \cdot)\)	None	0	12
296.2.bj	\(\chi_{296}(19, \cdot)\)	296.2.bj.a	432	12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(296))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(296)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(148))\)\(^{\oplus 2}\)