Space of modular forms of level 25 and weight 22

• Label: 25.22
• Level: 25
• Weight: 22
• Dimension: 474
• Nonzero newspaces: 4
• Sturm bound: 1100
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 25 = 5^{2} \)
Weight:	\( k \)	=	\( 22 \)
Nonzero newspaces:			\( 4 \)
Sturm bound:			\(1100\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_1(25))\).

	Total	New	Old
Modular forms	539	495	44
Cusp forms	511	474	37
Eisenstein series	28	21	7

Trace form

474 * q - 2342 * q^2 + 115654 * q^3 + 4277246 * q^4 - 6230615 * q^5 - 223119602 * q^6 - 89824302 * q^7 - 16125492250 * q^8 + 27695513349 * q^9 - 77467871440 * q^10 - 90909291862 * q^11 + 228060546198 * q^12 + 127151172224 * q^13 - 3941581051258 * q^14 + 2456204232480 * q^15 - 53092568118386 * q^16 + 18540332830868 * q^17 - 68727336674486 * q^18 + 61251365601370 * q^19 + 134718382674890 * q^20 - 83199240767802 * q^21 + 540777759201766 * q^22 - 69756630891326 * q^23 - 1374919577314580 * q^24 + 1045081743136435 * q^25 + 3507003478498428 * q^26 - 4840325760966830 * q^27 + 1261721251234806 * q^28 + 20747228465787920 * q^29 - 22500115425503210 * q^30 - 10481524206056322 * q^31 + 38166402429163958 * q^32 + 9020406018356838 * q^33 - 94224907544629378 * q^34 - 16855132182004200 * q^35 - 192391293143865546 * q^36 - 73410267185960917 * q^37 + 84980504907613900 * q^38 - 69616215961218402 * q^39 + 240967862773814540 * q^40 + 116804379150897408 * q^41 - 936751662072586694 * q^42 + 617382196460676694 * q^43 + 2187332842875500392 * q^44 - 3000680928567071875 * q^45 - 475609005650897942 * q^46 + 1586904218641044578 * q^47 + 660632602727098644 * q^48 - 4453931750216132094 * q^49 - 706374239263746750 * q^50 + 3811870119890511288 * q^51 + 172450597761941828 * q^52 - 8459176043573147741 * q^53 - 10164026886092557840 * q^54 + 14387571855754500990 * q^55 - 9078660141650366510 * q^56 - 37979676189083507770 * q^57 - 3856430841029184220 * q^58 + 37008483314801970790 * q^59 + 60905220210926788370 * q^60 - 23221602568273616052 * q^61 - 119127509042325903344 * q^62 + 124542235139379508694 * q^63 + 117772680086960736856 * q^64 - 109938761706438496325 * q^65 - 121282005806544620434 * q^66 + 7965673485843674238 * q^67 - 9096586225218242394 * q^68 + 193579087841152763398 * q^69 - 62299536771761729170 * q^70 - 191079162129722006322 * q^71 - 152049465896968234200 * q^72 + 140445523839928360604 * q^73 - 201400500012100196828 * q^74 + 122558609544378935860 * q^75 - 851424689057581247740 * q^76 - 472174706014286410794 * q^77 + 842324707628412144728 * q^78 + 809205951481195530950 * q^79 - 466470689128096795130 * q^80 - 2071600979886702222411 * q^81 - 1815697821211704814074 * q^82 + 1810762209749750804954 * q^83 + 2497920807748660742822 * q^84 - 1834321202615330982655 * q^85 - 1861799895531806195782 * q^86 - 806860196723775333310 * q^87 - 3178986250475170777090 * q^88 + 777000960873232441965 * q^89 + 7119582547288453957470 * q^90 - 1124976689772527213122 * q^91 - 11956812817314220877662 * q^92 - 2805218276921116168442 * q^93 + 6529437677311768292102 * q^94 + 1939555820506304271210 * q^95 - 9323136174262964635702 * q^96 + 766213838065080807928 * q^97 - 3507187440287480567994 * q^98 + 1109352691467373428768 * q^99

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_1(25))\)

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
25.22.a	\(\chi_{25}(1, \cdot)\)	25.22.a.a	1	1
		25.22.a.b	3
		25.22.a.c	4
		25.22.a.d	7
		25.22.a.e	7
		25.22.a.f	10
25.22.b	\(\chi_{25}(24, \cdot)\)	25.22.b.a	2	1
		25.22.b.b	6
		25.22.b.c	8
		25.22.b.d	14
25.22.d	\(\chi_{25}(6, \cdot)\)	n/a	204	4
25.22.e	\(\chi_{25}(4, \cdot)\)	n/a	208	4

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_1(25))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_1(25)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)