Space of modular forms of level 322 and weight 4

• Label: 322.4
• Level: 322
• Weight: 4
• Dimension: 3024
• Nonzero newspaces: 8
• Sturm bound: 25344
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(25344\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(322))\).

	Total	New	Old
Modular forms	9768	3024	6744
Cusp forms	9240	3024	6216
Eisenstein series	528	0	528

Trace form

3024 * q - 24 * q^3 + 48 * q^5 + 72 * q^6 + 96 * q^7 - 84 * q^9 - 72 * q^10 - 84 * q^11 - 96 * q^12 - 132 * q^13 - 264 * q^14 - 1472 * q^15 - 52 * q^17 + 512 * q^18 + 560 * q^19 + 944 * q^20 + 1464 * q^21 + 1400 * q^22 + 2230 * q^23 + 96 * q^24 + 988 * q^25 - 256 * q^26 - 888 * q^27 - 416 * q^28 - 2032 * q^29 - 3328 * q^30 - 2620 * q^31 - 2732 * q^33 + 816 * q^34 - 590 * q^35 + 336 * q^36 - 2460 * q^37 - 216 * q^38 + 768 * q^39 - 288 * q^40 + 2684 * q^41 - 648 * q^42 + 4464 * q^43 - 336 * q^44 + 6096 * q^45 + 168 * q^46 + 3820 * q^47 + 192 * q^48 + 2358 * q^49 - 48 * q^50 - 948 * q^51 - 624 * q^52 - 3088 * q^53 - 5960 * q^54 - 16656 * q^55 - 2032 * q^56 - 16728 * q^57 - 2688 * q^58 - 9372 * q^59 + 832 * q^60 + 432 * q^61 + 3192 * q^62 + 4276 * q^63 - 768 * q^64 + 21280 * q^65 + 11680 * q^66 + 9924 * q^67 + 7184 * q^68 + 16292 * q^69 + 7320 * q^70 + 15224 * q^71 + 6272 * q^72 + 5412 * q^73 + 3664 * q^74 - 424 * q^75 - 2928 * q^76 - 4892 * q^77 - 5208 * q^78 - 12352 * q^79 - 2048 * q^80 - 17328 * q^81 - 8064 * q^82 - 17896 * q^83 - 1960 * q^84 - 16276 * q^85 - 12152 * q^86 + 4764 * q^87 - 2688 * q^88 - 880 * q^89 - 4776 * q^90 + 2192 * q^91 + 432 * q^92 - 588 * q^93 + 1632 * q^94 - 636 * q^95 + 384 * q^96 - 14212 * q^97 - 1672 * q^98 - 15636 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(322))\)

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
322.4.a	\(\chi_{322}(1, \cdot)\)	322.4.a.a	2	1
		322.4.a.b	2
		322.4.a.c	2
		322.4.a.d	3
		322.4.a.e	3
		322.4.a.f	4
		322.4.a.g	5
		322.4.a.h	5
		322.4.a.i	6
322.4.c	\(\chi_{322}(321, \cdot)\)	322.4.c.a	24	1
		322.4.c.b	24
322.4.e	\(\chi_{322}(93, \cdot)\)	322.4.e.a	22	2
		322.4.e.b	22
		322.4.e.c	22
		322.4.e.d	22
322.4.g	\(\chi_{322}(45, \cdot)\)	322.4.g.a	48	2
		322.4.g.b	48
322.4.i	\(\chi_{322}(29, \cdot)\)	n/a	360	10
322.4.k	\(\chi_{322}(83, \cdot)\)	n/a	480	10
322.4.m	\(\chi_{322}(9, \cdot)\)	n/a	960	20
322.4.o	\(\chi_{322}(5, \cdot)\)	n/a	960	20

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(322))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(322)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 2}\)