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Properties

Label 25.6
Level 25
Weight 6
Dimension 105
Nonzero newspaces 4
Newform subspaces 8
Sturm bound 300
Trace bound 1

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Defining parameters

Level: \( N \) = \( 25 = 5^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 8 \)
Sturm bound: \(300\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(25))\).

Total New Old
Modular forms 139 126 13
Cusp forms 111 105 6
Eisenstein series 28 21 7

Trace form

\( 105 q - 14 q^{2} - 2 q^{3} + 94 q^{4} + 55 q^{5} - 530 q^{6} - 394 q^{7} + 230 q^{8} + 1056 q^{9} + O(q^{10}) \) \( 105 q - 14 q^{2} - 2 q^{3} + 94 q^{4} + 55 q^{5} - 530 q^{6} - 394 q^{7} + 230 q^{8} + 1056 q^{9} + 380 q^{10} - 730 q^{11} - 234 q^{12} - 582 q^{13} - 2362 q^{14} - 1230 q^{15} - 370 q^{16} + 1436 q^{17} + 8998 q^{18} + 7530 q^{19} + 10250 q^{20} + 7170 q^{21} - 8858 q^{22} - 15182 q^{23} - 46100 q^{24} - 19015 q^{25} - 11940 q^{26} - 6200 q^{27} + 28982 q^{28} + 48710 q^{29} + 53830 q^{30} + 1770 q^{31} + 25526 q^{32} + 6186 q^{33} - 35502 q^{34} - 40380 q^{35} - 59370 q^{36} - 30979 q^{37} - 72980 q^{38} + 18942 q^{39} + 89740 q^{40} + 61470 q^{41} + 203962 q^{42} + 62438 q^{43} + 55528 q^{44} - 17785 q^{45} - 4630 q^{46} - 42274 q^{47} - 276012 q^{48} - 201151 q^{49} - 252450 q^{50} - 78840 q^{51} - 108604 q^{52} - 71147 q^{53} + 11120 q^{54} + 91130 q^{55} + 167890 q^{56} + 296390 q^{57} + 305460 q^{58} + 164620 q^{59} + 97490 q^{60} - 31030 q^{61} + 93472 q^{62} + 86468 q^{63} + 136024 q^{64} + 136165 q^{65} + 55550 q^{66} - 3594 q^{67} + 76902 q^{68} - 184748 q^{69} - 117650 q^{70} - 276330 q^{71} - 663960 q^{72} - 126902 q^{73} - 177692 q^{74} - 310790 q^{75} - 349820 q^{76} - 257658 q^{77} - 257464 q^{78} - 178610 q^{79} + 1990 q^{80} + 77580 q^{81} - 334538 q^{82} + 89648 q^{83} + 798758 q^{84} + 681165 q^{85} + 993770 q^{86} + 1113980 q^{87} + 1558270 q^{88} + 572085 q^{89} + 754410 q^{90} + 68170 q^{91} - 528094 q^{92} - 390224 q^{93} - 617082 q^{94} - 423990 q^{95} - 380470 q^{96} - 918474 q^{97} - 1384098 q^{98} - 1089108 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(25))\)

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
25.6.a \(\chi_{25}(1, \cdot)\) 25.6.a.a 1 1
25.6.a.b 2
25.6.a.c 2
25.6.a.d 2
25.6.b \(\chi_{25}(24, \cdot)\) 25.6.b.a 2 1
25.6.b.b 4
25.6.d \(\chi_{25}(6, \cdot)\) 25.6.d.a 44 4
25.6.e \(\chi_{25}(4, \cdot)\) 25.6.e.a 48 4

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(25))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(25)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)