Space of modular forms of level 32 and weight 30

• Label: 32.30
• Level: 32
• Weight: 30
• Dimension: 517
• Nonzero newspaces: 3
• Sturm bound: 1920
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 32 = 2^{5} \)
Weight:	\( k \)	=	\( 30 \)
Nonzero newspaces:			\( 3 \)
Sturm bound:			\(1920\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{30}(\Gamma_1(32))\).

	Total	New	Old
Modular forms	944	527	417
Cusp forms	912	517	395
Eisenstein series	32	10	22

Trace form

517 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 8701963886 * q^5 - 4 * q^6 - 1356446145700 * q^7 - 4 * q^8 + 156832850543321 * q^9 + 339794921874996 * q^10 - 4 * q^11 + 20802213438104012 * q^12 + 4268937488690266 * q^13 - 131836345585488980 * q^14 + 116634443346832736 * q^15 - 1279630023291682224 * q^16 + 879289043939551090 * q^17 - 3953567272066360024 * q^18 - 4 * q^19 - 2399415917968750004 * q^20 - 35878598345025424644 * q^21 + 33973372616700239136 * q^22 - 307959310262823008348 * q^23 - 20425650072582626352 * q^24 + 94544137154567470235 * q^25 + 979550662582973532976 * q^26 + 1269049048665627408212 * q^27 + 1756803536895989834616 * q^28 + 2010959232001954541642 * q^29 + 16946248499876085416004 * q^30 + 25426700579426888945552 * q^31 + 19892968659171348231016 * q^32 + 11462207631472753071144 * q^33 - 17360955599214650049136 * q^34 - 88527677709753626283820 * q^35 - 379396099916191003856336 * q^36 - 128256412586339161080302 * q^37 + 17373842681255468271764 * q^38 + 76767982115413560149428 * q^39 + 156923143939176628763368 * q^40 + 207597626448828574319510 * q^41 + 1965663803696383392685576 * q^42 - 730959382927661996894012 * q^43 + 5262132319228689104589956 * q^44 - 3466173195360322189346778 * q^45 - 3283965668760017980613796 * q^46 - 121247766087237335010240 * q^47 - 8989296540073528270512912 * q^48 + 18094595184887114334098193 * q^49 + 46108104016008470469541716 * q^50 + 18830115476921620522075064 * q^51 - 63215535816912385760237532 * q^52 + 2376997595143970884355570 * q^53 - 93069006576790344450563936 * q^54 + 11737572287515920840083132 * q^55 + 145705455117678474153531304 * q^56 + 43043842506914757747016172 * q^57 + 142854815892019007994775584 * q^58 - 43791565559750425323128612 * q^59 - 642081709817383616729141768 * q^60 - 214430286447955584613948566 * q^61 + 292979790219899485572485880 * q^62 - 126882211730040892878949008 * q^63 - 291398560691528001855097384 * q^64 + 87650812044271966104276828 * q^65 - 1209811436043475396585735156 * q^66 - 971117338886725526166541164 * q^67 - 159183793147139580108984496 * q^68 + 2545214575869873268425034652 * q^69 - 5677394529106254692823902056 * q^70 - 1018842326910457595375660996 * q^71 + 10186308492210722659511996372 * q^72 + 1810725436142034863316541254 * q^73 - 5969753914442778462003092372 * q^74 + 7740941568904656996476939824 * q^75 - 5592695855578804733497395204 * q^76 - 4043005285566229085547623092 * q^77 - 9442344296888048568000542412 * q^78 + 2323214658985225396749618624 * q^79 + 16737762451072388504438333624 * q^80 + 21932215562377587248805062929 * q^81 + 14873551578983574511020646396 * q^82 - 16275793726181327023885778844 * q^83 - 70746621431956604895957734432 * q^84 - 25301009800781506221137668868 * q^85 + 47405691804480471624378992576 * q^86 + 108293626620793613250323032660 * q^87 - 37094095774136868754741747360 * q^88 - 79184261691524999669229443946 * q^89 + 82165837589410835854401899240 * q^90 + 129467255278527798833842218668 * q^91 - 171675795471814821939393996888 * q^92 + 49757462283824646167804044720 * q^93 + 338477729998084940355619411496 * q^94 + 191944615659014161746299398296 * q^95 + 520901190314533950239042275712 * q^96 - 108641488235686370876897353542 * q^97 + 351856964911028248506349032856 * q^98 + 519636415937137367632576654320 * q^99

Decomposition of \(S_{30}^{\mathrm{new}}(\Gamma_1(32))\)

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
32.30.a	\(\chi_{32}(1, \cdot)\)	32.30.a.a	1	1
		32.30.a.b	6
		32.30.a.c	7
		32.30.a.d	7
		32.30.a.e	8
32.30.b	\(\chi_{32}(17, \cdot)\)	32.30.b.a	28	1
32.30.e	\(\chi_{32}(9, \cdot)\)	None	0	2
32.30.g	\(\chi_{32}(5, \cdot)\)	n/a	460	4

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

Decomposition of \(S_{30}^{\mathrm{old}}(\Gamma_1(32))\) into lower level spaces

\( S_{30}^{\mathrm{old}}(\Gamma_1(32)) \cong \) \(S_{30}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{30}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 5}\)\(\oplus\)\(S_{30}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{30}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{30}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)