Space of modular forms of level 30 and weight 10

• Label: 30.10
• Level: 30
• Weight: 10
• Dimension: 52
• Nonzero newspaces: 3
• Newform subspaces: 9
• Sturm bound: 480
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	=	\( 10 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 9 \)
Sturm bound:			\(480\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(30))\).

	Total	New	Old
Modular forms	232	52	180
Cusp forms	200	52	148
Eisenstein series	32	0	32

Trace form

52 * q + 134 * q^3 - 1024 * q^4 + 1976 * q^5 + 7136 * q^6 + 11352 * q^7 - 26244 * q^9 + 27712 * q^10 + 54688 * q^11 - 117248 * q^12 - 12216 * q^13 - 113408 * q^14 + 21770 * q^15 - 1310720 * q^16 + 958536 * q^17 - 276352 * q^18 - 1051536 * q^19 - 505856 * q^20 + 2646896 * q^21 + 2308224 * q^22 + 1406376 * q^23 - 663552 * q^24 - 4364460 * q^25 + 1999872 * q^26 - 10050466 * q^27 + 2906112 * q^28 + 16020576 * q^29 + 9932064 * q^30 - 25966688 * q^31 - 26396176 * q^33 - 14372608 * q^34 - 8426096 * q^35 + 34657280 * q^36 + 50060184 * q^37 + 6132096 * q^38 + 7260516 * q^39 - 4669440 * q^40 - 152372144 * q^41 - 34535168 * q^42 + 151554984 * q^43 - 30570496 * q^44 + 175750456 * q^45 - 10553600 * q^46 - 20754288 * q^47 - 30015488 * q^48 + 7403700 * q^49 + 57308288 * q^50 + 113916892 * q^51 + 36870144 * q^52 - 212677488 * q^53 - 17006112 * q^54 - 359258656 * q^55 - 62095360 * q^56 + 48971048 * q^57 + 310381824 * q^58 + 31861960 * q^59 + 31230464 * q^60 + 88333592 * q^61 - 164548224 * q^62 + 123495632 * q^63 - 67108864 * q^64 - 793199232 * q^65 - 183168640 * q^66 + 453716040 * q^67 + 245385216 * q^68 + 455632128 * q^69 + 775120896 * q^70 + 27872928 * q^71 + 70746112 * q^72 - 722315136 * q^73 - 1107274112 * q^74 - 289290290 * q^75 + 144347136 * q^76 + 222155424 * q^77 + 929450688 * q^78 + 1955406552 * q^79 + 129499136 * q^80 - 2186080772 * q^81 - 1628419584 * q^82 - 1515103776 * q^83 - 251320320 * q^84 - 286741888 * q^85 - 472368256 * q^86 + 1776364796 * q^87 + 590905344 * q^88 + 859071272 * q^89 + 97492160 * q^90 + 5355502512 * q^91 + 360032256 * q^92 + 2891064608 * q^93 - 3645822464 * q^94 - 4691576280 * q^95 - 127926272 * q^96 - 4053436248 * q^97 - 329833728 * q^98 - 783488376 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(30))\)

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
30.10.a	\(\chi_{30}(1, \cdot)\)	30.10.a.a	1	1
		30.10.a.b	1
		30.10.a.c	1
		30.10.a.d	1
		30.10.a.e	1
		30.10.a.f	1
30.10.c	\(\chi_{30}(19, \cdot)\)	30.10.c.a	4	1
		30.10.c.b	6
30.10.e	\(\chi_{30}(17, \cdot)\)	30.10.e.a	36	2

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(30))\) into lower level spaces

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