Space of modular forms of level 23 and weight 13

• Label: 23.13
• Level: 23
• Weight: 13
• Dimension: 253
• Nonzero newspaces: 2
• Newform subspaces: 4
• Sturm bound: 572
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 23 \)
Weight:	\( k \)	=	\( 13 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 4 \)
Sturm bound:			\(572\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{13}(\Gamma_1(23))\).

	Total	New	Old
Modular forms	275	275	0
Cusp forms	253	253	0
Eisenstein series	22	22	0

Trace form

253 * 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 - 62475963 * q^15 + 95293429 * q^16 - 80926571 * q^17 + 153021429 * q^18 + 111165109 * q^19 - 272498699 * q^20 - 600623771 * q^21 + 648695509 * q^23 + 1642967018 * q^24 - 554361995 * q^25 - 1437765131 * q^26 - 721348331 * q^27 + 3957719029 * q^28 + 1286152549 * q^29 - 3340699659 * q^30 - 2846329211 * q^31 + 3825930229 * q^32 + 3117947349 * q^33 - 13971708113 * q^34 + 5952374989 * q^35 + 20606624764 * q^36 - 17898788171 * q^37 - 26779027286 * q^38 + 7541580805 * q^39 + 61210874989 * q^40 + 10673506789 * q^41 - 31821396761 * q^42 - 41404506011 * q^43 - 66452112342 * q^44 + 95430895549 * q^46 + 68725348538 * q^47 + 79448678573 * q^48 - 44826881627 * q^49 - 169189453136 * q^50 - 105406226651 * q^51 - 69154458461 * q^52 + 51469276309 * q^53 + 243641488893 * q^54 + 72464970853 * q^55 + 293616662416 * q^56 - 250324213931 * q^57 - 368388880706 * q^58 - 8207384339 * q^59 - 233131567141 * q^60 + 210924022837 * q^61 + 514816473589 * q^62 + 295298022789 * q^63 - 85261811723 * q^64 - 572376553067 * q^65 - 898520009904 * q^66 - 163067150411 * q^67 + 473498556069 * q^69 + 1235346917354 * q^70 + 712219883749 * q^71 + 629768899738 * q^72 - 166826901131 * q^73 - 311901254588 * q^74 - 4023714628043 * q^75 - 845476021610 * q^76 + 1996690386229 * q^77 + 3635414304819 * q^78 + 686225579413 * q^79 - 1205174134802 * q^80 - 4033886494363 * q^81 - 2043383696321 * q^82 - 415316705771 * q^83 + 7244741619995 * q^84 + 5849039441773 * q^85 - 200733189437 * q^86 - 3275269203371 * q^87 - 4135942853955 * q^88 - 3344097505331 * q^89 - 6933278864446 * q^90 + 3671001058714 * q^92 + 8439971139578 * q^93 + 6825771102128 * q^94 + 5731295760421 * q^95 - 7988018650040 * q^96 - 2782724911571 * q^97 - 1436224802771 * q^98 - 7415031217451 * q^99

Decomposition of \(S_{13}^{\mathrm{new}}(\Gamma_1(23))\)

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
23.13.b	\(\chi_{23}(22, \cdot)\)	23.13.b.a	1	1
		23.13.b.b	2
		23.13.b.c	20
23.13.d	\(\chi_{23}(5, \cdot)\)	23.13.d.a	230	10