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Properties

Label 25.20
Level 25
Weight 20
Dimension 428
Nonzero newspaces 4
Sturm bound 1000
Trace bound 2

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Defining parameters

Level: \( N \) = \( 25 = 5^{2} \)
Weight: \( k \) = \( 20 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(1000\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{20}(\Gamma_1(25))\).

Total New Old
Modular forms 489 449 40
Cusp forms 461 428 33
Eisenstein series 28 21 7

Trace form

\( 428 q + 1474 q^{2} - 11222 q^{3} - 1889218 q^{4} + 4183525 q^{5} - 66792914 q^{6} - 267469266 q^{7} + 2015513510 q^{8} - 8028691167 q^{9} + O(q^{10}) \) \( 428 q + 1474 q^{2} - 11222 q^{3} - 1889218 q^{4} + 4183525 q^{5} - 66792914 q^{6} - 267469266 q^{7} + 2015513510 q^{8} - 8028691167 q^{9} + 2839321200 q^{10} + 770248346 q^{11} - 20466286026 q^{12} - 9628492192 q^{13} - 493094434426 q^{14} + 512221761810 q^{15} - 3541104461682 q^{16} - 493546226566 q^{17} + 4739536656658 q^{18} - 5970628018010 q^{19} - 10723146933190 q^{20} + 15888804664506 q^{21} - 30807148836762 q^{22} - 11707959266822 q^{23} + 203688411854380 q^{24} - 49453672592265 q^{25} - 87918884049684 q^{26} + 374263636265560 q^{27} - 29450632779498 q^{28} - 30173426551300 q^{29} - 294875169146330 q^{30} + 875460605196426 q^{31} - 1147452875889226 q^{32} - 872614849845774 q^{33} + 1874810914441934 q^{34} - 871801440735660 q^{35} - 5160739000909962 q^{36} + 1251569633923809 q^{37} + 4111064247836380 q^{38} - 3402957943736154 q^{39} - 14192868439881460 q^{40} + 9299832662030856 q^{41} + 10215819166519738 q^{42} - 34287298072906422 q^{43} + 6066728427752584 q^{44} + 45371027503631105 q^{45} + 14204421234626186 q^{46} - 31926190713542866 q^{47} - 36428409702124332 q^{48} + 70293346743467392 q^{49} + 9399900361114050 q^{50} - 185064090124464 q^{51} + 79831797829554404 q^{52} - 8951566153097207 q^{53} + 8935681951059680 q^{54} - 42304453508419030 q^{55} + 203592088242049810 q^{56} + 121866349332465590 q^{57} + 616924890483902500 q^{58} - 453415628200281800 q^{59} - 1900526775722532190 q^{60} + 879743748525553336 q^{61} + 1656167415934432768 q^{62} - 994483408450149892 q^{63} - 1996260393936477288 q^{64} - 702556492231032845 q^{65} + 2282107315890599342 q^{66} + 2274096691856647874 q^{67} - 763585391777041818 q^{68} - 2262294281374108064 q^{69} - 2509484002664436930 q^{70} + 4028921441156750766 q^{71} + 7599053955249521880 q^{72} - 2230638745046498732 q^{73} - 5176690144979243756 q^{74} + 1778639896717408210 q^{75} + 7255945661118182340 q^{76} + 689151554672743878 q^{77} - 7911696702220530424 q^{78} - 10950535240910383170 q^{79} + 17952129761653971910 q^{80} + 7727561739380311833 q^{81} + 3323657255952511158 q^{82} - 11899670893268567212 q^{83} - 22076874783379459546 q^{84} - 12063705251133365065 q^{85} + 21641664572425169786 q^{86} + 24229677309935114420 q^{87} - 10477683068035720770 q^{88} - 16972609832888688495 q^{89} - 26689910660165144850 q^{90} - 12668389250194835894 q^{91} + 29183868217356653474 q^{92} + 51000743463641412436 q^{93} + 38541479762805285254 q^{94} - 45253755859031678790 q^{95} - 56827798378032594454 q^{96} - 42067723642927312816 q^{97} + 47758515090510635502 q^{98} + 188905851861011151216 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{20}^{\mathrm{new}}(\Gamma_1(25))\)

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
25.20.a \(\chi_{25}(1, \cdot)\) 25.20.a.a 1 1
25.20.a.b 3
25.20.a.c 4
25.20.a.d 6
25.20.a.e 6
25.20.a.f 8
25.20.b \(\chi_{25}(24, \cdot)\) 25.20.b.a 2 1
25.20.b.b 6
25.20.b.c 8
25.20.b.d 12
25.20.d \(\chi_{25}(6, \cdot)\) n/a 188 4
25.20.e \(\chi_{25}(4, \cdot)\) n/a 184 4

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

Decomposition of \(S_{20}^{\mathrm{old}}(\Gamma_1(25))\) into lower level spaces

\( S_{20}^{\mathrm{old}}(\Gamma_1(25)) \cong \) \(S_{20}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)