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Properties

Label 35.3
Level 35
Weight 3
Dimension 70
Nonzero newspaces 6
Newform subspaces 9
Sturm bound 288
Trace bound 2

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Defining parameters

Level: \( N \) = \( 35 = 5 \cdot 7 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 9 \)
Sturm bound: \(288\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(35))\).

Total New Old
Modular forms 120 98 22
Cusp forms 72 70 2
Eisenstein series 48 28 20

Trace form

\( 70 q - 6 q^{2} - 12 q^{3} - 22 q^{4} - 12 q^{5} - 24 q^{6} + 2 q^{7} - 18 q^{8} - 30 q^{9} + O(q^{10}) \) \( 70 q - 6 q^{2} - 12 q^{3} - 22 q^{4} - 12 q^{5} - 24 q^{6} + 2 q^{7} - 18 q^{8} - 30 q^{9} - 12 q^{10} - 12 q^{11} - 12 q^{12} - 12 q^{13} - 54 q^{14} - 24 q^{15} - 2 q^{16} - 12 q^{17} + 42 q^{18} - 12 q^{19} - 12 q^{20} - 24 q^{21} - 60 q^{22} - 48 q^{23} + 180 q^{24} + 46 q^{25} + 168 q^{26} + 240 q^{27} + 346 q^{28} + 204 q^{29} + 276 q^{30} + 48 q^{31} + 42 q^{32} + 48 q^{33} - 48 q^{35} - 330 q^{36} - 44 q^{37} - 204 q^{38} - 312 q^{39} - 444 q^{40} - 192 q^{41} - 588 q^{42} - 356 q^{43} - 432 q^{44} - 408 q^{45} - 204 q^{46} - 168 q^{47} - 444 q^{48} - 110 q^{49} + 126 q^{50} - 24 q^{51} + 180 q^{52} + 420 q^{54} + 324 q^{55} + 558 q^{56} + 552 q^{57} + 720 q^{58} + 468 q^{59} + 1068 q^{60} + 552 q^{61} + 744 q^{62} + 690 q^{63} + 878 q^{64} + 276 q^{65} + 408 q^{66} + 416 q^{67} + 168 q^{68} - 192 q^{70} - 372 q^{71} - 546 q^{72} - 396 q^{73} - 900 q^{74} - 588 q^{75} - 1032 q^{76} - 672 q^{77} - 1320 q^{78} - 784 q^{79} - 1008 q^{80} - 1050 q^{81} - 1572 q^{82} - 684 q^{83} - 1020 q^{84} - 792 q^{85} - 60 q^{86} + 168 q^{87} + 336 q^{88} + 888 q^{89} + 900 q^{90} + 600 q^{91} + 1524 q^{92} + 912 q^{93} + 948 q^{94} + 852 q^{95} + 1320 q^{96} + 492 q^{97} + 1146 q^{98} + 564 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(35))\)

We only show spaces with odd 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
35.3.c \(\chi_{35}(34, \cdot)\) 35.3.c.a 1 1
35.3.c.b 1
35.3.c.c 4
35.3.d \(\chi_{35}(6, \cdot)\) 35.3.d.a 2 1
35.3.d.b 2
35.3.g \(\chi_{35}(8, \cdot)\) 35.3.g.a 12 2
35.3.h \(\chi_{35}(26, \cdot)\) 35.3.h.a 12 2
35.3.i \(\chi_{35}(19, \cdot)\) 35.3.i.a 12 2
35.3.l \(\chi_{35}(2, \cdot)\) 35.3.l.a 24 4

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(35))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(35)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 1}\)