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Properties

Label 25.8
Level 25
Weight 8
Dimension 151
Nonzero newspaces 4
Newform subspaces 10
Sturm bound 400
Trace bound 1

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Defining parameters

Level: \( N \) = \( 25 = 5^{2} \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 10 \)
Sturm bound: \(400\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(25))\).

Total New Old
Modular forms 189 172 17
Cusp forms 161 151 10
Eisenstein series 28 21 7

Trace form

\( 151 q - 22 q^{2} + 46 q^{3} - 386 q^{4} - 35 q^{5} + 2062 q^{6} + 3478 q^{7} - 4570 q^{8} - 15924 q^{9} + O(q^{10}) \) \( 151 q - 22 q^{2} + 46 q^{3} - 386 q^{4} - 35 q^{5} + 2062 q^{6} + 3478 q^{7} - 4570 q^{8} - 15924 q^{9} - 1560 q^{10} + 17862 q^{11} + 53238 q^{12} - 14814 q^{13} - 79162 q^{14} - 8910 q^{15} - 6514 q^{16} + 143008 q^{17} + 86626 q^{18} - 123910 q^{19} - 309670 q^{20} - 209478 q^{21} - 178554 q^{22} + 404466 q^{23} + 1367980 q^{24} + 446835 q^{25} - 147588 q^{26} - 895760 q^{27} - 1401386 q^{28} - 329850 q^{29} - 945050 q^{30} - 593078 q^{31} + 945078 q^{32} + 2054562 q^{33} + 2381798 q^{34} - 139420 q^{35} - 881994 q^{36} - 1384157 q^{37} - 901540 q^{38} + 1378782 q^{39} + 2620940 q^{40} + 687022 q^{41} - 2497094 q^{42} - 3363914 q^{43} - 8397752 q^{44} - 3473515 q^{45} + 4287242 q^{46} + 3184798 q^{47} + 8681556 q^{48} + 1278199 q^{49} + 8958650 q^{50} + 2972232 q^{51} + 4173348 q^{52} + 4777211 q^{53} - 11273920 q^{54} - 5520550 q^{55} - 13305710 q^{56} - 16620250 q^{57} - 11571980 q^{58} - 7671900 q^{59} + 18699650 q^{60} + 5584082 q^{61} + 30259776 q^{62} + 20269556 q^{63} + 5707544 q^{64} - 11933665 q^{65} - 16586866 q^{66} - 20731002 q^{67} - 23354266 q^{68} - 6482528 q^{69} - 5968290 q^{70} - 4975018 q^{71} + 33254520 q^{72} + 13693106 q^{73} + 28673508 q^{74} + 28907410 q^{75} + 25801540 q^{76} + 7556166 q^{77} - 15930808 q^{78} - 12899570 q^{79} - 48504250 q^{80} - 22088184 q^{81} - 64074234 q^{82} - 17217864 q^{83} + 11623718 q^{84} + 51064175 q^{85} + 41008122 q^{86} + 82366460 q^{87} + 21995070 q^{88} - 26015445 q^{89} - 60427770 q^{90} - 20358438 q^{91} - 115601502 q^{92} - 132708428 q^{93} - 57253882 q^{94} + 15736810 q^{95} + 35035562 q^{96} + 97782198 q^{97} + 201394774 q^{98} + 141831852 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(25))\)

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
25.8.a \(\chi_{25}(1, \cdot)\) 25.8.a.a 1 1
25.8.a.b 2
25.8.a.c 2
25.8.a.d 2
25.8.a.e 2
25.8.b \(\chi_{25}(24, \cdot)\) 25.8.b.a 2 1
25.8.b.b 4
25.8.b.c 4
25.8.d \(\chi_{25}(6, \cdot)\) 25.8.d.a 68 4
25.8.e \(\chi_{25}(4, \cdot)\) 25.8.e.a 64 4

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(25))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(25)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)