Space of modular forms of level 23 and weight 7

• Label: 23.7
• Level: 23
• Weight: 7
• Dimension: 121
• Nonzero newspaces: 2
• Newform subspaces: 4
• Sturm bound: 308
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 23 \)
Weight:	\( k \)	=	\( 7 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 4 \)
Sturm bound:			\(308\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(23))\).

	Total	New	Old
Modular forms	143	143	0
Cusp forms	121	121	0
Eisenstein series	22	22	0

Trace form

121 * 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 + 10461 * q^15 - 31691 * q^16 - 11451 * q^17 + 13365 * q^18 + 15829 * q^19 + 78837 * q^20 + 40909 * q^21 - 32923 * q^23 - 179542 * q^24 - 69707 * q^25 - 54571 * q^26 - 18491 * q^27 + 101365 * q^28 + 58509 * q^29 + 311157 * q^30 + 59389 * q^31 - 59851 * q^32 - 234267 * q^33 + 400015 * q^34 - 71511 * q^35 - 601436 * q^36 - 446699 * q^37 - 275286 * q^38 + 64141 * q^39 + 626989 * q^40 + 235389 * q^41 + 1274119 * q^42 + 428989 * q^43 + 434434 * q^44 - 542531 * q^46 - 518430 * q^47 - 1390675 * q^48 - 1141283 * q^49 - 1203136 * q^50 - 463331 * q^51 - 247181 * q^52 + 183909 * q^53 + 3219117 * q^54 + 1417405 * q^55 + 175560 * q^56 + 78661 * q^57 - 970706 * q^58 - 1638087 * q^59 - 2858581 * q^60 + 495253 * q^61 + 1544389 * q^62 + 1713789 * q^63 + 2973685 * q^64 + 2406085 * q^65 + 2124936 * q^66 + 290389 * q^67 - 770451 * q^69 - 2392918 * q^70 - 2086931 * q^71 - 5921630 * q^72 - 1024331 * q^73 - 1038180 * q^74 + 1483669 * q^75 - 1754258 * q^76 - 2268651 * q^77 - 6512781 * q^78 - 833723 * q^79 + 2796838 * q^80 + 138413 * q^81 + 3609199 * q^82 + 2924229 * q^83 + 6932651 * q^84 + 4488385 * q^85 + 1596771 * q^86 + 9184549 * q^87 + 5363325 * q^88 + 2950849 * q^89 + 5004362 * q^90 - 2477486 * q^92 - 6461422 * q^93 - 6892600 * q^94 - 3255219 * q^95 - 13057616 * q^96 - 6375215 * q^97 - 11621907 * q^98 - 16096091 * q^99

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(23))\)

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
23.7.b	\(\chi_{23}(22, \cdot)\)	23.7.b.a	1	1
		23.7.b.b	2
		23.7.b.c	8
23.7.d	\(\chi_{23}(5, \cdot)\)	23.7.d.a	110	10