Space of modular forms of level 23 and weight 4

• Label: 23.4
• Level: 23
• Weight: 4
• Dimension: 55
• Nonzero newspaces: 2
• Newform subspaces: 3
• Sturm bound: 176
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 23 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 3 \)
Sturm bound:			\(176\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(23))\).

	Total	New	Old
Modular forms	77	75	2
Cusp forms	55	55	0
Eisenstein series	22	20	2

Trace form

55 * q - 11 * q^2 - 11 * q^3 - 11 * q^4 - 11 * q^5 - 11 * q^6 - 11 * q^7 - 11 * q^8 - 11 * q^9 - 11 * q^10 - 11 * q^11 - 11 * q^12 - 11 * q^13 - 11 * q^14 - 385 * q^15 - 451 * q^16 - 99 * q^17 + 77 * q^18 + 99 * q^19 + 693 * q^20 + 649 * q^21 + 462 * q^22 + 473 * q^23 + 1298 * q^24 + 341 * q^25 + 209 * q^26 + 55 * q^27 - 363 * q^28 - 231 * q^29 - 1507 * q^30 - 561 * q^31 - 1507 * q^32 - 979 * q^33 - 1925 * q^34 - 1441 * q^35 - 2486 * q^36 - 1199 * q^37 - 616 * q^38 + 121 * q^39 + 1309 * q^40 + 539 * q^41 + 3619 * q^42 + 1705 * q^43 + 3212 * q^44 + 2948 * q^45 + 3949 * q^46 + 1870 * q^47 + 3333 * q^48 + 2167 * q^49 + 1914 * q^50 + 649 * q^51 + 319 * q^52 - 253 * q^53 - 5511 * q^54 - 4499 * q^55 - 9394 * q^56 - 5951 * q^57 - 7964 * q^58 - 3993 * q^59 - 4081 * q^60 + 517 * q^61 + 1705 * q^62 + 2079 * q^63 + 4213 * q^64 + 4301 * q^65 + 5148 * q^66 + 1441 * q^67 + 8954 * q^68 + 3729 * q^69 + 5786 * q^70 + 3399 * q^71 + 7084 * q^72 + 1045 * q^73 + 968 * q^74 - 5973 * q^75 - 7150 * q^76 - 5467 * q^77 - 11473 * q^78 - 4719 * q^79 - 11110 * q^80 - 6391 * q^81 - 4961 * q^82 - 3861 * q^83 - 5973 * q^84 + 891 * q^85 + 1463 * q^86 + 9361 * q^87 + 6237 * q^88 + 5599 * q^89 + 18502 * q^90 + 7986 * q^91 + 8998 * q^92 + 11726 * q^93 + 8316 * q^94 + 4015 * q^95 + 4092 * q^96 - 2321 * q^97 - 2651 * q^98 - 2321 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(23))\)

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
23.4.a	\(\chi_{23}(1, \cdot)\)	23.4.a.a	1	1
		23.4.a.b	4
23.4.c	\(\chi_{23}(2, \cdot)\)	23.4.c.a	50	10