Space of modular forms of level 30 and weight 12

• Label: 30.12
• Level: 30
• Weight: 12
• Dimension: 60
• Nonzero newspaces: 3
• Newform subspaces: 9
• Sturm bound: 576
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	=	\( 12 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 9 \)
Sturm bound:			\(576\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(30))\).

	Total	New	Old
Modular forms	280	60	220
Cusp forms	248	60	188
Eisenstein series	32	0	32

Trace form

60 * q - 1498 * q^3 - 4096 * q^4 - 4976 * q^5 - 18496 * q^6 - 20336 * q^7 - 236196 * q^9 - 62080 * q^10 + 2081744 * q^11 + 538624 * q^12 + 3705792 * q^13 - 670720 * q^14 + 843602 * q^15 - 29360128 * q^16 - 21550488 * q^17 - 10875136 * q^18 + 49249968 * q^19 + 5095424 * q^20 + 366008 * q^21 - 71727872 * q^22 + 45621048 * q^23 + 15925248 * q^24 + 406211260 * q^25 + 59927040 * q^26 - 86291482 * q^27 - 20824064 * q^28 + 467465232 * q^29 - 109960896 * q^30 + 255259008 * q^31 + 926790392 * q^33 + 333754880 * q^34 + 596470304 * q^35 + 891932672 * q^36 - 1431349392 * q^37 + 671202048 * q^38 + 1223675100 * q^39 + 282722304 * q^40 + 1505625200 * q^41 + 129977344 * q^42 - 2185406688 * q^43 - 533454848 * q^44 - 6852114344 * q^45 + 3693072384 * q^46 + 5009608464 * q^47 + 551550976 * q^48 - 6348369996 * q^49 - 7711429376 * q^50 - 4180882148 * q^51 - 3143565312 * q^52 - 8291982864 * q^53 + 918330048 * q^54 + 43199700272 * q^55 + 4509663232 * q^56 + 11859970736 * q^57 - 33384644608 * q^58 - 38870993080 * q^59 - 12170475520 * q^60 + 25765614920 * q^61 - 9367519488 * q^62 + 61483248416 * q^63 - 4294967296 * q^64 - 11802287952 * q^65 - 28189627648 * q^66 - 105803922320 * q^67 - 22067699712 * q^68 + 32128071984 * q^69 + 2455649280 * q^70 + 15626146944 * q^71 + 11136139264 * q^72 - 24257622328 * q^73 + 30390885632 * q^74 - 29594370146 * q^75 - 28047278080 * q^76 - 47362762752 * q^77 + 56239284864 * q^78 + 52149127464 * q^79 - 5217714176 * q^80 + 61351345924 * q^81 + 76670067712 * q^82 + 31416264192 * q^83 + 78015799296 * q^84 + 258305369832 * q^85 - 52654781696 * q^86 - 132711954148 * q^87 - 73449340928 * q^88 - 246390317336 * q^89 + 15125016704 * q^90 - 79743750048 * q^91 + 46715953152 * q^92 + 198560237744 * q^93 + 240449087488 * q^94 + 31236665304 * q^95 - 13220446208 * q^96 + 489713467344 * q^97 - 192888159744 * q^98 - 30761694648 * q^99

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(30))\)

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
30.12.a	\(\chi_{30}(1, \cdot)\)	30.12.a.a	1	1
		30.12.a.b	1
		30.12.a.c	1
		30.12.a.d	1
		30.12.a.e	1
		30.12.a.f	1
30.12.c	\(\chi_{30}(19, \cdot)\)	30.12.c.a	4	1
		30.12.c.b	6
30.12.e	\(\chi_{30}(17, \cdot)\)	30.12.e.a	44	2

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(30))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(30)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)