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Properties

Label 25.16
Level 25
Weight 16
Dimension 336
Nonzero newspaces 4
Sturm bound 800
Trace bound 2

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Defining parameters

Level: \( N \) = \( 25 = 5^{2} \)
Weight: \( k \) = \( 16 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(800\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(25))\).

Total New Old
Modular forms 389 357 32
Cusp forms 361 336 25
Eisenstein series 28 21 7

Trace form

\( 336 q - 46 q^{2} - 482 q^{3} - 84418 q^{4} + 264355 q^{5} - 638738 q^{6} + 184834 q^{7} + 6197030 q^{8} - 9658647 q^{9} + O(q^{10}) \) \( 336 q - 46 q^{2} - 482 q^{3} - 84418 q^{4} + 264355 q^{5} - 638738 q^{6} + 184834 q^{7} + 6197030 q^{8} - 9658647 q^{9} + 61549680 q^{10} - 87258318 q^{11} - 377734026 q^{12} + 1066336688 q^{13} - 1009919866 q^{14} + 15627120 q^{15} - 5610154354 q^{16} - 3110421476 q^{17} + 6776021218 q^{18} - 16953922990 q^{19} + 34457130650 q^{20} + 45465270342 q^{21} - 89991924762 q^{22} - 29493489102 q^{23} + 240590612140 q^{24} + 22107831985 q^{25} - 99157876788 q^{26} + 15546532690 q^{27} + 965462598742 q^{28} - 709508455920 q^{29} - 770949440570 q^{30} - 32338687618 q^{31} + 2950171486134 q^{32} - 544883536314 q^{33} - 4456855963026 q^{34} - 101416073080 q^{35} + 4926744873846 q^{36} + 2962981141529 q^{37} - 9539148923140 q^{38} - 9327050385234 q^{39} + 7347038249740 q^{40} + 5699365955632 q^{41} + 6953378033338 q^{42} + 4512194194878 q^{43} - 23311317930296 q^{44} - 9765590765185 q^{45} + 11173787636682 q^{46} + 25641267552994 q^{47} + 16048460757588 q^{48} - 36121361634408 q^{49} + 25135480266050 q^{50} + 52712771836392 q^{51} + 6487826553124 q^{52} - 79402466025967 q^{53} - 28798462532800 q^{54} + 41214265811230 q^{55} + 193504197304210 q^{56} + 11710501324550 q^{57} - 278170658674780 q^{58} - 132351236550690 q^{59} + 191018468820290 q^{60} + 26986261743332 q^{61} + 245934834116448 q^{62} - 35334573756442 q^{63} - 153094634465768 q^{64} - 376368765658735 q^{65} - 212508435264466 q^{66} - 29573408459786 q^{67} + 823794215104742 q^{68} + 539703600837046 q^{69} - 580354158258850 q^{70} - 475699858440418 q^{71} - 1227099623351880 q^{72} + 286749060754388 q^{73} + 2725998687046644 q^{74} + 826212780117460 q^{75} - 1715128675963580 q^{76} - 1709445175110282 q^{77} - 1070611990455064 q^{78} + 927372070763110 q^{79} + 1565264979166790 q^{80} - 1889600464359759 q^{81} + 1586072995721878 q^{82} - 1080551884347102 q^{83} + 162835358520614 q^{84} + 2068473543530715 q^{85} - 377596453272198 q^{86} - 3524090150749390 q^{87} + 286353719793470 q^{88} - 847970631089505 q^{89} + 29999000778510 q^{90} - 354457033668098 q^{91} + 10837308328388514 q^{92} - 173657072014394 q^{93} - 7425883444735866 q^{94} - 5382840752783990 q^{95} - 1267675699390678 q^{96} + 1618943245685544 q^{97} + 2913160782562942 q^{98} + 7997399568934536 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(25))\)

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
25.16.a \(\chi_{25}(1, \cdot)\) 25.16.a.a 1 1
25.16.a.b 2
25.16.a.c 3
25.16.a.d 5
25.16.a.e 5
25.16.a.f 6
25.16.b \(\chi_{25}(24, \cdot)\) 25.16.b.a 2 1
25.16.b.b 4
25.16.b.c 6
25.16.b.d 10
25.16.d \(\chi_{25}(6, \cdot)\) n/a 148 4
25.16.e \(\chi_{25}(4, \cdot)\) n/a 144 4

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

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_1(25))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_1(25)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 1}\)