Space of modular forms of level 15 and weight 25

• Label: 15.25
• Level: 15
• Weight: 25
• Dimension: 126
• Nonzero newspaces: 3
• Newform subspaces: 5
• Sturm bound: 400
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	=	\( 25 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(400\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{25}(\Gamma_1(15))\).

	Total	New	Old
Modular forms	200	130	70
Cusp forms	184	126	58
Eisenstein series	16	4	12

Trace form

126 * q + 605360 * q^3 + 93139160 * q^4 + 826763616 * q^5 + 7268847232 * q^6 - 14248163360 * q^7 - 267070377420 * q^8 + 1696542638638 * q^9 + 2390295762284 * q^10 - 6955017870528 * q^11 + 26154151638580 * q^12 - 83859922904240 * q^13 - 222614321098786 * q^15 + 2303034112879360 * q^16 - 2026039851939600 * q^17 + 1867332841187240 * q^18 + 320088211646556 * q^19 - 22273864612799436 * q^20 + 33759924674027712 * q^21 - 90067793695912440 * q^22 + 84780359882864640 * q^23 - 228215354000405976 * q^24 - 313872930681464034 * q^25 + 726693661661140656 * q^26 - 135678077168238640 * q^27 + 1449204129178921480 * q^28 - 1575755111272222124 * q^30 + 8058114154938983964 * q^31 - 6027324512812012620 * q^32 - 5689065873306996320 * q^33 + 22318958168890717144 * q^34 + 9363928959035280000 * q^35 + 14575401362943752288 * q^36 + 14647697089375030960 * q^37 + 51457505793803161920 * q^38 - 91011282275750112736 * q^39 + 29446045488137064688 * q^40 - 24807448352223415872 * q^41 - 215497981116243015600 * q^42 - 11853540513308934560 * q^43 + 96030336296234230576 * q^45 - 210633152000077065080 * q^46 - 162622409158522051200 * q^47 + 539890651660275986140 * q^48 + 480484972890454275982 * q^49 - 1406662212652210263456 * q^50 + 830333745705145331260 * q^51 - 1736421708108925397000 * q^52 + 1707050148630849015120 * q^53 - 4011141351344286143408 * q^54 - 2980626818491395415104 * q^55 + 9134967764421991572480 * q^56 + 3882470489270118262880 * q^57 - 14644770351585097543320 * q^58 + 22768047255522109294936 * q^60 - 22717500863776311934884 * q^61 - 3224099222158299460920 * q^62 + 18647745396986673813120 * q^63 + 7638480378080116982664 * q^64 - 3420436597755403985712 * q^65 - 46251794954937255270832 * q^66 + 48198426148098742666720 * q^67 + 60352516164608230308480 * q^68 - 45305124902193572972868 * q^69 - 19190398196193186402600 * q^70 - 22958205695684496883584 * q^71 - 59712167617402330405620 * q^72 + 114458683184680974023920 * q^73 - 29293488430501365895216 * q^75 - 70413996183496659092768 * q^76 + 106087825205397981771840 * q^77 - 126086650004859942726080 * q^78 + 306202091476291816572636 * q^79 - 593940915794696334392556 * q^80 - 619380044135724194688674 * q^81 + 326280889571305658162040 * q^82 + 539352556907762085465600 * q^83 + 48758340933144432720504 * q^84 - 364876122864094334735188 * q^85 - 1083568040031040642222848 * q^86 + 467938418545781774366720 * q^87 + 2089312889294641193548200 * q^88 - 752507970900885853661116 * q^90 - 4788278376093106844341312 * q^91 + 5737655065352213932504200 * q^92 + 1454408365333151190486720 * q^93 - 4871985956826637016969336 * q^94 - 103729985725161089079936 * q^95 + 858083445384612495317600 * q^96 + 1563922232779695513187120 * q^97 + 11500728192903685199057640 * q^98 + 4825095383573473004753600 * q^99

Decomposition of \(S_{25}^{\mathrm{new}}(\Gamma_1(15))\)

We only show spaces with odd 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
15.25.c	\(\chi_{15}(11, \cdot)\)	15.25.c.a	32	1
15.25.d	\(\chi_{15}(14, \cdot)\)	15.25.d.a	1	1
		15.25.d.b	1
		15.25.d.c	44
15.25.f	\(\chi_{15}(7, \cdot)\)	15.25.f.a	48	2

Decomposition of \(S_{25}^{\mathrm{old}}(\Gamma_1(15))\) into lower level spaces

\( S_{25}^{\mathrm{old}}(\Gamma_1(15)) \cong \) \(S_{25}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{25}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{25}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)