Properties

Label 35.6
Level 35
Weight 6
Dimension 196
Nonzero newspaces 6
Newform subspaces 10
Sturm bound 576
Trace bound 2

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Defining parameters

Level: \( N \) = \( 35 = 5 \cdot 7 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 10 \)
Sturm bound: \(576\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(35))\).

Total New Old
Modular forms 264 228 36
Cusp forms 216 196 20
Eisenstein series 48 32 16

Trace form

\( 196 q - 10 q^{2} + 20 q^{3} - 30 q^{4} + 154 q^{5} - 92 q^{6} + 34 q^{7} + 570 q^{8} - 728 q^{9} + O(q^{10}) \) \( 196 q - 10 q^{2} + 20 q^{3} - 30 q^{4} + 154 q^{5} - 92 q^{6} + 34 q^{7} + 570 q^{8} - 728 q^{9} - 774 q^{10} - 1144 q^{11} + 4384 q^{12} + 4092 q^{13} + 2298 q^{14} - 3376 q^{15} - 3482 q^{16} - 1504 q^{17} - 6694 q^{18} + 4756 q^{19} + 3932 q^{20} + 5388 q^{21} + 208 q^{22} - 13812 q^{23} - 27408 q^{24} - 10070 q^{25} - 3592 q^{26} + 19568 q^{27} + 51754 q^{28} + 59512 q^{29} + 64462 q^{30} - 4632 q^{31} - 56042 q^{32} - 100988 q^{33} - 143100 q^{34} - 78486 q^{35} - 115066 q^{36} + 13900 q^{37} + 70436 q^{38} + 98840 q^{39} + 118676 q^{40} + 100264 q^{41} + 200280 q^{42} + 86400 q^{43} + 106444 q^{44} - 34688 q^{45} - 43780 q^{46} - 147088 q^{47} - 175496 q^{48} - 87568 q^{49} - 112522 q^{50} - 22712 q^{51} - 42932 q^{52} - 65080 q^{53} + 73744 q^{54} - 63628 q^{55} - 70278 q^{56} + 86864 q^{57} + 182360 q^{58} + 302900 q^{59} + 515104 q^{60} + 231844 q^{61} + 333600 q^{62} + 141546 q^{63} + 121174 q^{64} - 178208 q^{65} - 768148 q^{66} - 345388 q^{67} - 402836 q^{68} - 389808 q^{69} - 687858 q^{70} - 418880 q^{71} - 768942 q^{72} - 394320 q^{73} - 92384 q^{74} + 242324 q^{75} + 363604 q^{76} + 224304 q^{77} + 988312 q^{78} + 427020 q^{79} + 810104 q^{80} + 1065352 q^{81} + 685160 q^{82} + 357780 q^{83} - 267504 q^{84} - 319092 q^{85} - 790648 q^{86} - 880552 q^{87} - 631500 q^{88} - 191772 q^{89} + 80684 q^{90} + 154796 q^{91} + 1176216 q^{92} + 907764 q^{93} + 731232 q^{94} + 399400 q^{95} + 752612 q^{96} - 346676 q^{97} - 244586 q^{98} + 121976 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(35))\)

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
35.6.a \(\chi_{35}(1, \cdot)\) 35.6.a.a 1 1
35.6.a.b 2
35.6.a.c 3
35.6.a.d 4
35.6.b \(\chi_{35}(29, \cdot)\) 35.6.b.a 14 1
35.6.e \(\chi_{35}(11, \cdot)\) 35.6.e.a 12 2
35.6.e.b 16
35.6.f \(\chi_{35}(13, \cdot)\) 35.6.f.a 36 2
35.6.j \(\chi_{35}(4, \cdot)\) 35.6.j.a 36 2
35.6.k \(\chi_{35}(3, \cdot)\) 35.6.k.a 72 4

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(35))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(35)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)