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Properties

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

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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

\( 474 q - 2342 q^{2} + 115654 q^{3} + 4277246 q^{4} - 6230615 q^{5} - 223119602 q^{6} - 89824302 q^{7} - 16125492250 q^{8} + 27695513349 q^{9} + O(q^{10}) \) \( 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} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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