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Properties

Label 35.7
Level 35
Weight 7
Dimension 238
Nonzero newspaces 6
Newform subspaces 8
Sturm bound 672
Trace bound 1

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Defining parameters

Level: \( N \) = \( 35 = 5 \cdot 7 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 8 \)
Sturm bound: \(672\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(35))\).

Total New Old
Modular forms 312 266 46
Cusp forms 264 238 26
Eisenstein series 48 28 20

Trace form

\( 238 q + 14 q^{2} - 66 q^{3} - 6 q^{4} - 37 q^{5} + 1080 q^{6} + 404 q^{7} - 2322 q^{8} + 3690 q^{9} + O(q^{10}) \) \( 238 q + 14 q^{2} - 66 q^{3} - 6 q^{4} - 37 q^{5} + 1080 q^{6} + 404 q^{7} - 2322 q^{8} + 3690 q^{9} + 6148 q^{10} - 6146 q^{11} - 18900 q^{12} - 3932 q^{13} + 22290 q^{14} + 16986 q^{15} + 21574 q^{16} - 9910 q^{17} - 66690 q^{18} - 59982 q^{19} - 40692 q^{20} + 71202 q^{21} + 174836 q^{22} + 87758 q^{23} - 8604 q^{24} - 87269 q^{25} - 257840 q^{26} - 240060 q^{27} - 58094 q^{28} + 80772 q^{29} + 442836 q^{30} + 278174 q^{31} + 580562 q^{32} + 217050 q^{33} - 177203 q^{35} - 933114 q^{36} - 851990 q^{37} - 971964 q^{38} - 19668 q^{39} + 212316 q^{40} + 527296 q^{41} + 405060 q^{42} + 94840 q^{43} + 1038744 q^{44} + 635442 q^{45} + 114068 q^{46} + 281078 q^{47} - 411564 q^{48} - 657102 q^{49} + 138986 q^{50} - 862338 q^{51} + 138028 q^{52} - 65926 q^{53} + 648852 q^{54} + 527324 q^{55} - 530394 q^{56} - 898620 q^{57} - 1654656 q^{58} - 642774 q^{59} - 3277992 q^{60} - 265954 q^{61} + 2567464 q^{62} + 3165324 q^{63} + 4877334 q^{64} + 3128696 q^{65} + 3518496 q^{66} - 598898 q^{67} - 1354664 q^{68} - 599352 q^{70} - 186764 q^{71} - 5822322 q^{72} - 4707158 q^{73} - 6718620 q^{74} - 4247733 q^{75} - 724008 q^{76} - 2193178 q^{77} - 602808 q^{78} + 1895370 q^{79} + 5214392 q^{80} + 2904240 q^{81} + 170636 q^{82} + 2950856 q^{83} + 10006236 q^{84} + 4774438 q^{85} + 4792276 q^{86} + 2357640 q^{87} - 3335472 q^{88} + 840834 q^{89} - 12996840 q^{90} - 4817540 q^{91} - 8339452 q^{92} - 11041062 q^{93} - 1495500 q^{94} - 597633 q^{95} + 8826312 q^{96} + 5973292 q^{97} + 10038750 q^{98} + 7625220 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(35))\)

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
35.7.c \(\chi_{35}(34, \cdot)\) 35.7.c.a 1 1
35.7.c.b 1
35.7.c.c 20
35.7.d \(\chi_{35}(6, \cdot)\) 35.7.d.a 16 1
35.7.g \(\chi_{35}(8, \cdot)\) 35.7.g.a 36 2
35.7.h \(\chi_{35}(26, \cdot)\) 35.7.h.a 32 2
35.7.i \(\chi_{35}(19, \cdot)\) 35.7.i.a 44 2
35.7.l \(\chi_{35}(2, \cdot)\) 35.7.l.a 88 4

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(35))\) into lower level spaces

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