Space of modular forms of level 10 and weight 18

• Label: 10.18
• Level: 10
• Weight: 18
• Dimension: 15
• Nonzero newspaces: 2
• Newform subspaces: 5
• Sturm bound: 108
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	=	\( 18 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(108\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_1(10))\).

	Total	New	Old
Modular forms	55	15	40
Cusp forms	47	15	32
Eisenstein series	8	0	8

Trace form

15 * q - 256 * q^2 - 4964 * q^3 - 65536 * q^4 - 1616185 * q^5 + 1653760 * q^6 + 49640552 * q^7 - 16777216 * q^8 + 83530787 * q^9 - 240779520 * q^10 - 156359820 * q^11 - 325320704 * q^12 - 5259218734 * q^13 + 23308859392 * q^14 - 50597815220 * q^15 + 64424509440 * q^16 - 1140224898 * q^17 + 55132074752 * q^18 + 30010351340 * q^19 + 54718300160 * q^20 + 602945547280 * q^21 - 445042363392 * q^22 - 82347597864 * q^23 + 236156092416 * q^24 + 2081341012975 * q^25 - 2217149795840 * q^26 + 3526468806520 * q^27 + 3253243215872 * q^28 + 1767644488290 * q^29 + 776089205760 * q^30 - 2211184896320 * q^31 - 1099511627776 * q^32 - 24080865991248 * q^33 + 7013607173632 * q^34 - 16075049405960 * q^35 + 53077330821120 * q^36 - 90600510737158 * q^37 + 25686817745920 * q^38 + 59855872248104 * q^39 + 2672526622720 * q^40 - 262219118254170 * q^41 + 9278596538368 * q^42 + 48708157195796 * q^43 - 29414130450432 * q^44 + 319349657012955 * q^45 - 158410528675840 * q^46 - 468908924842368 * q^47 - 21320217657344 * q^48 + 1392353718892983 * q^49 + 496347408531200 * q^50 - 2092241531371720 * q^51 - 344668158951424 * q^52 + 771768939695466 * q^53 + 4185494603520000 * q^54 + 272552059988980 * q^55 - 341582104494080 * q^56 - 4894114504687120 * q^57 + 1130080958784000 * q^58 + 3150568987496580 * q^59 + 1902653618257920 * q^60 - 7493802825602670 * q^61 - 6675522216353792 * q^62 + 7955317090432616 * q^63 - 281474976710656 * q^64 + 7767887360563330 * q^65 - 11169896844308480 * q^66 - 12767118471683908 * q^67 - 74725778915328 * q^68 + 38879977645480624 * q^69 - 1744670477240320 * q^70 - 34642830450121320 * q^71 + 3613135650947072 * q^72 - 13995582151311034 * q^73 - 8025570039408128 * q^74 + 16669874150260700 * q^75 + 9079272734720000 * q^76 - 12354227646083136 * q^77 + 4600556316166144 * q^78 + 1561762545712880 * q^79 - 6941461719285760 * q^80 + 71472071253034215 * q^81 + 3612164220016128 * q^82 + 22441018762155756 * q^83 - 28045418091773952 * q^84 - 58557333008926610 * q^85 + 22967805037941760 * q^86 + 142187591241889800 * q^87 - 29166296327258112 * q^88 - 126907617221623290 * q^89 - 14157771982736640 * q^90 + 209629933000184080 * q^91 - 5396732173615104 * q^92 - 202446187448100448 * q^93 - 5897113360150528 * q^94 - 26299615368010100 * q^95 + 7102845115432960 * q^96 + 363067859693827022 * q^97 - 198820889786956032 * q^98 - 678890389608404956 * q^99

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_1(10))\)

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
10.18.a	\(\chi_{10}(1, \cdot)\)	10.18.a.a	1	1
		10.18.a.b	2
		10.18.a.c	2
		10.18.a.d	2
10.18.b	\(\chi_{10}(9, \cdot)\)	10.18.b.a	8	1

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_1(10))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_1(10)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 1}\)