Space of modular forms of level 2116 and weight 2

• Label: 2116.2
• Level: 2116
• Weight: 2
• Dimension: 80454
• Nonzero newspaces: 8
• Sturm bound: 558624
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 2116 = 2^{2} \cdot 23^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(558624\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2116))\).

	Total	New	Old
Modular forms	141526	81862	59664
Cusp forms	137787	80454	57333
Eisenstein series	3739	1408	2331

Trace form

80454 * q - 231 * q^2 - 231 * q^4 - 462 * q^5 - 231 * q^6 - 231 * q^8 - 462 * q^9 - 231 * q^10 - 231 * q^12 - 462 * q^13 - 231 * q^14 + 22 * q^15 - 231 * q^16 - 440 * q^17 - 231 * q^18 + 22 * q^19 - 231 * q^20 - 396 * q^21 - 253 * q^22 + 22 * q^23 - 451 * q^24 - 418 * q^25 - 231 * q^26 + 66 * q^27 - 231 * q^28 - 440 * q^29 - 231 * q^30 + 22 * q^31 - 231 * q^32 - 440 * q^33 - 275 * q^34 - 44 * q^35 - 341 * q^36 - 550 * q^37 - 341 * q^38 - 88 * q^39 - 407 * q^40 - 506 * q^41 - 451 * q^42 - 88 * q^43 - 385 * q^44 - 638 * q^45 - 330 * q^46 - 88 * q^47 - 407 * q^48 - 594 * q^49 - 385 * q^50 - 88 * q^51 - 451 * q^52 - 506 * q^53 - 407 * q^54 - 44 * q^55 - 341 * q^56 - 484 * q^57 - 341 * q^58 + 44 * q^59 - 275 * q^60 - 374 * q^61 - 231 * q^62 + 110 * q^63 - 231 * q^64 - 308 * q^65 - 165 * q^66 + 44 * q^67 - 253 * q^68 - 429 * q^69 - 451 * q^70 + 110 * q^71 - 297 * q^72 - 418 * q^73 - 209 * q^74 + 110 * q^75 - 121 * q^76 - 528 * q^77 - 11 * q^78 + 44 * q^79 - 33 * q^80 - 638 * q^81 - 99 * q^82 + 22 * q^83 + 77 * q^84 - 726 * q^85 - 11 * q^86 - 132 * q^87 - 55 * q^88 - 594 * q^89 + 143 * q^90 - 88 * q^91 - 143 * q^92 - 1430 * q^93 - 77 * q^94 - 66 * q^95 + 187 * q^96 - 528 * q^97 - 55 * q^98 - 22 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2116))\)

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
2116.2.a	\(\chi_{2116}(1, \cdot)\)	2116.2.a.a	1	1
		2116.2.a.b	1
		2116.2.a.c	1
		2116.2.a.d	1
		2116.2.a.e	2
		2116.2.a.f	2
		2116.2.a.g	6
		2116.2.a.h	8
		2116.2.a.i	10
		2116.2.a.j	10
2116.2.b	\(\chi_{2116}(2115, \cdot)\)	n/a	232	1
2116.2.e	\(\chi_{2116}(177, \cdot)\)	n/a	420	10
2116.2.h	\(\chi_{2116}(63, \cdot)\)	n/a	2320	10
2116.2.i	\(\chi_{2116}(93, \cdot)\)	n/a	1012	22
2116.2.l	\(\chi_{2116}(91, \cdot)\)	n/a	6028	22
2116.2.m	\(\chi_{2116}(9, \cdot)\)	n/a	10120	220
2116.2.n	\(\chi_{2116}(7, \cdot)\)	n/a	60280	220

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2116))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2116)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(529))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1058))\)\(^{\oplus 2}\)