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

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

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 the 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

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