Space of modular forms of level 10 and weight 12

• Label: 10.12
• Level: 10
• Weight: 12
• Dimension: 11
• Nonzero newspaces: 2
• Newform subspaces: 5
• Sturm bound: 72
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	=	\( 12 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(72\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(10))\).

	Total	New	Old
Modular forms	37	11	26
Cusp forms	29	11	18
Eisenstein series	8	0	8

Trace form

11 * q + 32 * q^2 + 1012 * q^3 - 1024 * q^4 + 3655 * q^5 + 2944 * q^6 - 45224 * q^7 + 32768 * q^8 - 159637 * q^9 - 285920 * q^10 + 29932 * q^11 + 1036288 * q^12 - 2191418 * q^13 - 4302592 * q^14 - 161180 * q^15 + 11534336 * q^16 + 12748506 * q^17 - 1427296 * q^18 - 53745980 * q^19 + 2657280 * q^20 + 101555152 * q^21 + 20705664 * q^22 - 98981928 * q^23 - 31850496 * q^24 - 132890725 * q^25 + 135891904 * q^26 + 423112600 * q^27 - 46309376 * q^28 - 550255470 * q^29 - 54314880 * q^30 + 112946752 * q^31 + 33554432 * q^32 + 134433024 * q^33 - 656797632 * q^34 - 556336360 * q^35 + 852384768 * q^36 + 403327246 * q^37 - 247560320 * q^38 + 2412868856 * q^39 + 497582080 * q^40 - 953091338 * q^41 - 1984111616 * q^42 - 1784459588 * q^43 + 1346957312 * q^44 + 2403558015 * q^45 - 2910183936 * q^46 - 1770523344 * q^47 + 1061158912 * q^48 + 7729962807 * q^49 + 4224762400 * q^50 - 11266516408 * q^51 - 2244012032 * q^52 + 219799902 * q^53 - 1802184960 * q^54 - 505693140 * q^55 - 51904512 * q^56 - 13068201520 * q^57 + 4214028480 * q^58 + 24462502060 * q^59 + 1265848320 * q^60 + 4035983482 * q^61 + 7243427584 * q^62 - 23253311128 * q^63 - 1073741824 * q^64 - 7992223130 * q^65 - 18111375872 * q^66 + 12541795636 * q^67 + 13054470144 * q^68 - 3407357504 * q^69 + 37412426240 * q^70 + 62154676392 * q^71 - 1461551104 * q^72 - 48488064638 * q^73 - 86491899712 * q^74 - 85616347900 * q^75 - 5660487680 * q^76 + 103920657552 * q^77 + 77720217088 * q^78 - 16354527920 * q^79 + 3832545280 * q^80 + 116916257331 * q^81 - 6817242816 * q^82 - 87174300588 * q^83 - 152972525568 * q^84 - 146862254310 * q^85 - 4125330816 * q^86 + 10614977880 * q^87 + 21202599936 * q^88 + 274708176590 * q^89 + 309751163040 * q^90 - 135806542768 * q^91 - 101357494272 * q^92 - 88457439856 * q^93 - 377363722752 * q^94 - 17026181900 * q^95 + 3087007744 * q^96 - 17065411814 * q^97 + 467353825056 * q^98 + 667711166156 * q^99

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(10))\)

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
10.12.a	\(\chi_{10}(1, \cdot)\)	10.12.a.a	1	1
		10.12.a.b	1
		10.12.a.c	1
		10.12.a.d	2
10.12.b	\(\chi_{10}(9, \cdot)\)	10.12.b.a	6	1

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(10))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(10)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 1}\)