Space of modular forms of level 2952 and weight 1

• Label: 2952.1
• Level: 2952
• Weight: 1
• Dimension: 211
• Nonzero newspaces: 15
• Newform subspaces: 25
• Sturm bound: 483840
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 2952 = 2^{3} \cdot 3^{2} \cdot 41 \)
Weight:	\( k \)	=	\( 1 \)
Nonzero newspaces:			\( 15 \)
Newform subspaces:			\( 25 \)
Sturm bound:			\(483840\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2952))\).

	Total	New	Old
Modular forms	4476	913	3563
Cusp forms	636	211	425
Eisenstein series	3840	702	3138

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	191	0	4	16

Trace form

211 * q + 3 * q^2 - 6 * q^3 + 7 * q^4 + 2 * q^6 - 4 * q^7 - 3 * q^8 - 6 * q^9 - 4 * q^10 - 2 * q^11 + 4 * q^13 + 8 * q^14 - q^16 + 18 * q^17 - 10 * q^19 - 4 * q^22 + 2 * q^24 + 5 * q^25 - 12 * q^26 + 12 * q^27 - 4 * q^28 + 2 * q^30 + 4 * q^31 + 3 * q^32 - 12 * q^33 - 8 * q^34 - 4 * q^35 + 4 * q^37 + 8 * q^39 + 8 * q^40 - 2 * q^41 - 16 * q^42 + 22 * q^44 + 4 * q^46 + 4 * q^47 + 4 * q^48 - 3 * q^49 + 3 * q^50 - 8 * q^51 + 2 * q^54 - 2 * q^56 + 8 * q^57 - 2 * q^58 - 2 * q^59 + 4 * q^62 - 5 * q^64 - 6 * q^65 + 8 * q^66 + 14 * q^67 - 8 * q^68 - 2 * q^72 - 10 * q^73 + 2 * q^74 + 2 * q^75 - 10 * q^76 - 2 * q^78 + 4 * q^79 - 2 * q^81 + 5 * q^82 + 10 * q^83 + 4 * q^87 - 4 * q^88 - 14 * q^89 + 2 * q^90 - 4 * q^96 - 8 * q^97 - 7 * q^98 + 8 * q^99

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2952))\)

We only show spaces with odd 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
2952.1.b	\(\chi_{2952}(737, \cdot)\)	None	0	1
2952.1.c	\(\chi_{2952}(739, \cdot)\)	None	0	1
2952.1.h	\(\chi_{2952}(163, \cdot)\)	2952.1.h.a	1	1
		2952.1.h.b	2
		2952.1.h.c	2
2952.1.i	\(\chi_{2952}(1313, \cdot)\)	None	0	1
2952.1.l	\(\chi_{2952}(2215, \cdot)\)	None	0	1
2952.1.m	\(\chi_{2952}(2213, \cdot)\)	None	0	1
2952.1.n	\(\chi_{2952}(2789, \cdot)\)	None	0	1
2952.1.o	\(\chi_{2952}(1639, \cdot)\)	None	0	1
2952.1.r	\(\chi_{2952}(1567, \cdot)\)	None	0	2
2952.1.s	\(\chi_{2952}(2141, \cdot)\)	None	0	2
2952.1.v	\(\chi_{2952}(91, \cdot)\)	2952.1.v.a	2	2
2952.1.w	\(\chi_{2952}(665, \cdot)\)	2952.1.w.a	4	2
2952.1.bb	\(\chi_{2952}(821, \cdot)\)	None	0	2
2952.1.bc	\(\chi_{2952}(655, \cdot)\)	None	0	2
2952.1.bd	\(\chi_{2952}(247, \cdot)\)	None	0	2
2952.1.be	\(\chi_{2952}(245, \cdot)\)	2952.1.be.a	8	2
2952.1.bh	\(\chi_{2952}(1147, \cdot)\)	2952.1.bh.a	2	2
		2952.1.bh.b	2
2952.1.bi	\(\chi_{2952}(329, \cdot)\)	None	0	2
2952.1.bn	\(\chi_{2952}(1721, \cdot)\)	None	0	2
2952.1.bo	\(\chi_{2952}(1723, \cdot)\)	None	0	2
2952.1.bp	\(\chi_{2952}(109, \cdot)\)	2952.1.bp.a	4	4
2952.1.bq	\(\chi_{2952}(577, \cdot)\)	None	0	4
2952.1.br	\(\chi_{2952}(683, \cdot)\)	None	0	4
2952.1.bs	\(\chi_{2952}(1151, \cdot)\)	None	0	4
2952.1.by	\(\chi_{2952}(127, \cdot)\)	None	0	4
2952.1.bz	\(\chi_{2952}(1205, \cdot)\)	None	0	4
2952.1.ca	\(\chi_{2952}(269, \cdot)\)	None	0	4
2952.1.cb	\(\chi_{2952}(631, \cdot)\)	None	0	4
2952.1.ce	\(\chi_{2952}(305, \cdot)\)	None	0	4
2952.1.cf	\(\chi_{2952}(523, \cdot)\)	2952.1.cf.a	4	4
2952.1.ck	\(\chi_{2952}(379, \cdot)\)	2952.1.ck.a	4	4
2952.1.cl	\(\chi_{2952}(1097, \cdot)\)	None	0	4
2952.1.co	\(\chi_{2952}(401, \cdot)\)	None	0	4
2952.1.cp	\(\chi_{2952}(1075, \cdot)\)	2952.1.cp.a	4	4
		2952.1.cp.b	4
2952.1.cs	\(\chi_{2952}(173, \cdot)\)	None	0	4
2952.1.ct	\(\chi_{2952}(319, \cdot)\)	None	0	4
2952.1.cx	\(\chi_{2952}(377, \cdot)\)	None	0	8
2952.1.cy	\(\chi_{2952}(307, \cdot)\)	2952.1.cy.a	8	8
2952.1.db	\(\chi_{2952}(125, \cdot)\)	None	0	8
2952.1.dc	\(\chi_{2952}(415, \cdot)\)	None	0	8
2952.1.dh	\(\chi_{2952}(659, \cdot)\)	2952.1.dh.a	8	8
		2952.1.dh.b	8
2952.1.di	\(\chi_{2952}(167, \cdot)\)	None	0	8
2952.1.dj	\(\chi_{2952}(85, \cdot)\)	None	0	8
2952.1.dk	\(\chi_{2952}(601, \cdot)\)	None	0	8
2952.1.dl	\(\chi_{2952}(139, \cdot)\)	2952.1.dl.a	8	8
		2952.1.dl.b	8
		2952.1.dl.c	16
2952.1.dm	\(\chi_{2952}(113, \cdot)\)	None	0	8
2952.1.dr	\(\chi_{2952}(713, \cdot)\)	None	0	8
2952.1.ds	\(\chi_{2952}(187, \cdot)\)	2952.1.ds.a	8	8
		2952.1.ds.b	8
2952.1.dv	\(\chi_{2952}(605, \cdot)\)	None	0	8
2952.1.dw	\(\chi_{2952}(223, \cdot)\)	None	0	8
2952.1.dx	\(\chi_{2952}(31, \cdot)\)	None	0	8
2952.1.dy	\(\chi_{2952}(221, \cdot)\)	None	0	8
2952.1.ee	\(\chi_{2952}(71, \cdot)\)	None	0	16
2952.1.ef	\(\chi_{2952}(35, \cdot)\)	None	0	16
2952.1.eg	\(\chi_{2952}(145, \cdot)\)	None	0	16
2952.1.eh	\(\chi_{2952}(181, \cdot)\)	None	0	16
2952.1.ei	\(\chi_{2952}(103, \cdot)\)	None	0	16
2952.1.ej	\(\chi_{2952}(5, \cdot)\)	None	0	16
2952.1.em	\(\chi_{2952}(43, \cdot)\)	2952.1.em.a	16	16
		2952.1.em.b	16
2952.1.en	\(\chi_{2952}(185, \cdot)\)	None	0	16
2952.1.eq	\(\chi_{2952}(97, \cdot)\)	None	0	32
2952.1.er	\(\chi_{2952}(13, \cdot)\)	None	0	32
2952.1.es	\(\chi_{2952}(47, \cdot)\)	None	0	32
2952.1.et	\(\chi_{2952}(11, \cdot)\)	2952.1.et.a	32	32
		2952.1.et.b	32

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2952))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2952)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(123))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(164))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(246))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(328))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(369))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(492))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(738))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(984))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1476))\)\(^{\oplus 2}\)