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Properties

Label 35.9
Level 35
Weight 9
Dimension 322
Nonzero newspaces 6
Newform subspaces 8
Sturm bound 864
Trace bound 1

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Defining parameters

Level: \( N \) = \( 35 = 5 \cdot 7 \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 8 \)
Sturm bound: \(864\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(35))\).

Total New Old
Modular forms 408 350 58
Cusp forms 360 322 38
Eisenstein series 48 28 20

Trace form

\( 322 q - 2 q^{2} + 300 q^{3} - 1030 q^{4} + 388 q^{5} - 3528 q^{6} - 5038 q^{7} + 24510 q^{8} + 2322 q^{9} + O(q^{10}) \) \( 322 q - 2 q^{2} + 300 q^{3} - 1030 q^{4} + 388 q^{5} - 3528 q^{6} - 5038 q^{7} + 24510 q^{8} + 2322 q^{9} - 67548 q^{10} - 31948 q^{11} + 173628 q^{12} + 238272 q^{13} - 29454 q^{14} - 687672 q^{15} - 791546 q^{16} + 813904 q^{17} + 2315838 q^{18} + 515076 q^{19} - 824532 q^{20} - 2271048 q^{21} - 2070876 q^{22} - 1134200 q^{23} + 2576628 q^{24} + 1545358 q^{25} + 4645760 q^{26} + 1021488 q^{27} - 3712958 q^{28} - 4888452 q^{29} - 785412 q^{30} + 2863872 q^{31} - 1222526 q^{32} - 5083224 q^{33} + 5915960 q^{35} + 8588694 q^{36} + 1078480 q^{37} + 19490964 q^{38} + 20548608 q^{39} - 21791292 q^{40} - 17580400 q^{41} - 59190684 q^{42} - 12493076 q^{43} + 11530584 q^{44} + 34171008 q^{45} + 22618164 q^{46} + 11096536 q^{47} + 23200020 q^{48} - 1518326 q^{49} - 33884822 q^{50} - 26977992 q^{51} - 20012532 q^{52} - 21799364 q^{53} - 28951356 q^{54} + 29997924 q^{55} + 12365190 q^{56} - 7672488 q^{57} + 54139008 q^{58} + 6770028 q^{59} + 128663184 q^{60} - 30722112 q^{61} + 9145256 q^{62} + 115843914 q^{63} - 20102794 q^{64} - 65106140 q^{65} - 231804720 q^{66} - 240238984 q^{67} - 264838408 q^{68} + 334611288 q^{70} + 297196412 q^{71} + 491865870 q^{72} - 145635456 q^{73} - 86059068 q^{74} + 255590808 q^{75} + 15035544 q^{76} - 140012600 q^{77} - 410065752 q^{78} - 112885864 q^{79} - 474292424 q^{80} - 72214134 q^{81} + 210776700 q^{82} + 289157332 q^{83} + 563857884 q^{84} + 277630860 q^{85} + 79432964 q^{86} - 398684544 q^{87} - 643096752 q^{88} - 572030880 q^{89} - 633311160 q^{90} - 143287944 q^{91} + 596940964 q^{92} + 1276066824 q^{93} + 1529849604 q^{94} + 699311664 q^{95} + 815496168 q^{96} + 212024832 q^{97} - 1147068498 q^{98} - 2507336220 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(35))\)

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
35.9.c \(\chi_{35}(34, \cdot)\) 35.9.c.a 1 1
35.9.c.b 1
35.9.c.c 28
35.9.d \(\chi_{35}(6, \cdot)\) 35.9.d.a 20 1
35.9.g \(\chi_{35}(8, \cdot)\) 35.9.g.a 48 2
35.9.h \(\chi_{35}(26, \cdot)\) 35.9.h.a 44 2
35.9.i \(\chi_{35}(19, \cdot)\) 35.9.i.a 60 2
35.9.l \(\chi_{35}(2, \cdot)\) 35.9.l.a 120 4

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(35))\) into lower level spaces

\( S_{9}^{\mathrm{old}}(\Gamma_1(35)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)