Space of modular forms of level 1011 and weight 4

• Label: 1011.4
• Level: 1011
• Weight: 4
• Dimension: 84840
• Nonzero newspaces: 20
• Sturm bound: 302848
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 1011 = 3 \cdot 337 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 20 \)
Sturm bound:			\(302848\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1011))\).

	Total	New	Old
Modular forms	114240	85512	28728
Cusp forms	112896	84840	28056
Eisenstein series	1344	672	672

Trace form

84840 * q - 168 * q^3 - 336 * q^4 - 168 * q^6 - 336 * q^7 - 168 * q^9 - 336 * q^10 - 168 * q^12 - 336 * q^13 - 168 * q^15 - 336 * q^16 - 168 * q^18 - 336 * q^19 - 168 * q^21 - 336 * q^22 - 168 * q^24 - 336 * q^25 - 168 * q^27 - 336 * q^28 - 168 * q^30 - 336 * q^31 - 168 * q^33 - 336 * q^34 - 168 * q^36 - 336 * q^37 - 168 * q^39 - 336 * q^40 - 168 * q^42 - 336 * q^43 - 168 * q^45 - 336 * q^46 - 168 * q^48 - 336 * q^49 - 168 * q^51 - 336 * q^52 - 168 * q^54 - 336 * q^55 - 168 * q^57 - 336 * q^58 - 168 * q^60 - 336 * q^61 - 168 * q^63 - 336 * q^64 - 168 * q^66 - 336 * q^67 - 168 * q^69 - 336 * q^70 - 168 * q^72 - 336 * q^73 - 168 * q^75 - 336 * q^76 - 168 * q^78 - 336 * q^79 - 168 * q^81 - 336 * q^82 - 168 * q^84 - 336 * q^85 - 168 * q^87 - 336 * q^88 - 168 * q^90 - 336 * q^91 - 168 * q^93 - 336 * q^94 - 168 * q^96 - 336 * q^97 - 168 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1011))\)

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
1011.4.a	\(\chi_{1011}(1, \cdot)\)	1011.4.a.a	34	1
		1011.4.a.b	38
		1011.4.a.c	46
		1011.4.a.d	50
1011.4.d	\(\chi_{1011}(673, \cdot)\)	n/a	168	1
1011.4.e	\(\chi_{1011}(208, \cdot)\)	n/a	336	2
1011.4.g	\(\chi_{1011}(148, \cdot)\)	n/a	336	2
1011.4.h	\(\chi_{1011}(466, \cdot)\)	n/a	336	2
1011.4.k	\(\chi_{1011}(52, \cdot)\)	n/a	1008	6
1011.4.m	\(\chi_{1011}(85, \cdot)\)	n/a	680	4
1011.4.n	\(\chi_{1011}(220, \cdot)\)	n/a	672	4
1011.4.p	\(\chi_{1011}(379, \cdot)\)	n/a	1008	6
1011.4.s	\(\chi_{1011}(59, \cdot)\)	n/a	2688	8
1011.4.u	\(\chi_{1011}(4, \cdot)\)	n/a	2016	12
1011.4.v	\(\chi_{1011}(172, \cdot)\)	n/a	1360	8
1011.4.x	\(\chi_{1011}(49, \cdot)\)	n/a	2016	12
1011.4.bb	\(\chi_{1011}(358, \cdot)\)	n/a	2016	12
1011.4.bd	\(\chi_{1011}(38, \cdot)\)	n/a	5376	16
1011.4.be	\(\chi_{1011}(7, \cdot)\)	n/a	4080	24
1011.4.bh	\(\chi_{1011}(37, \cdot)\)	n/a	4032	24
1011.4.bj	\(\chi_{1011}(5, \cdot)\)	n/a	16128	48
1011.4.bl	\(\chi_{1011}(28, \cdot)\)	n/a	8160	48
1011.4.bm	\(\chi_{1011}(20, \cdot)\)	n/a	32256	96

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1011))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1011)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(337))\)\(^{\oplus 2}\)