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Properties

Label 35.17
Level 35
Weight 17
Dimension 658
Nonzero newspaces 6
Sturm bound 1632
Trace bound 1

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Defining parameters

Level: \( N \) = \( 35 = 5 \cdot 7 \)
Weight: \( k \) = \( 17 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(1632\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{17}(\Gamma_1(35))\).

Total New Old
Modular forms 792 686 106
Cusp forms 744 658 86
Eisenstein series 48 28 20

Trace form

\( 658 q - 2 q^{2} - 28944 q^{3} + 262138 q^{4} - 627662 q^{5} - 8834760 q^{6} - 1378330 q^{7} - 18368514 q^{8} - 294410718 q^{9} + O(q^{10}) \) \( 658 q - 2 q^{2} - 28944 q^{3} + 262138 q^{4} - 627662 q^{5} - 8834760 q^{6} - 1378330 q^{7} - 18368514 q^{8} - 294410718 q^{9} - 229875868 q^{10} - 245208136 q^{11} + 534824316 q^{12} + 1362717152 q^{13} - 2212565262 q^{14} - 5013322212 q^{15} + 71064190726 q^{16} - 59206964708 q^{17} + 41659267326 q^{18} + 59506153776 q^{19} + 40373640108 q^{20} - 285967860756 q^{21} + 499970013028 q^{22} + 58245754516 q^{23} - 1175372993484 q^{24} + 374125359208 q^{25} + 754161735104 q^{26} + 572408079288 q^{27} - 3477052518398 q^{28} - 1350187588308 q^{29} + 744125266908 q^{30} + 3724379901484 q^{31} + 4425822274114 q^{32} - 2569025455812 q^{33} + 13349765189210 q^{35} - 2278611985194 q^{36} - 14654243336804 q^{37} + 3760544958804 q^{38} + 6391457660040 q^{39} + 5791898765028 q^{40} - 72976157859184 q^{41} - 63695386859292 q^{42} + 65111922904900 q^{43} + 66028633462872 q^{44} - 117083396443692 q^{45} - 140359952035532 q^{46} - 91021567170140 q^{47} + 776467733847060 q^{48} + 94391464116938 q^{49} - 887466443431382 q^{50} - 543109426268940 q^{51} + 526329347516300 q^{52} + 485633863624240 q^{53} + 1304540507000580 q^{54} - 1302353947741676 q^{55} - 528339358007034 q^{56} - 41148761017776 q^{57} + 1339212811727232 q^{58} + 1335384501719592 q^{59} - 1238644896677136 q^{60} - 1065571033657844 q^{61} - 1081018446602584 q^{62} - 1694836773419442 q^{63} + 1304991876433654 q^{64} + 1136857561711180 q^{65} + 1196110725046416 q^{66} - 1443772090379100 q^{67} - 2285956255509640 q^{68} + 8388827232402648 q^{70} - 468220231010932 q^{71} - 8292793709335794 q^{72} - 4819534672449748 q^{73} + 3171499773846852 q^{74} + 1915769644081998 q^{75} + 6913155294841752 q^{76} + 1180191774228436 q^{77} - 24970184644253400 q^{78} - 16858116313611332 q^{79} + 24963882956188216 q^{80} + 12606195547538526 q^{81} + 33836684165650492 q^{82} - 8300457426464228 q^{83} - 43512964099034148 q^{84} - 15479873932725400 q^{85} - 12989121072546364 q^{86} + 17418351168779424 q^{87} + 68321146494557520 q^{88} + 33184544044004148 q^{89} + 1554339929983560 q^{90} - 19619767155095584 q^{91} - 170113543480622300 q^{92} - 38026836986897700 q^{93} - 33929375045310780 q^{94} + 45222460165376334 q^{95} + 271169252863733352 q^{96} + 34378839418331072 q^{97} - 168570447202374354 q^{98} - 158557684651809852 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{17}^{\mathrm{new}}(\Gamma_1(35))\)

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
35.17.c \(\chi_{35}(34, \cdot)\) 35.17.c.a 1 1
35.17.c.b 1
35.17.c.c 60
35.17.d \(\chi_{35}(6, \cdot)\) 35.17.d.a 44 1
35.17.g \(\chi_{35}(8, \cdot)\) 35.17.g.a 96 2
35.17.h \(\chi_{35}(26, \cdot)\) 35.17.h.a 84 2
35.17.i \(\chi_{35}(19, \cdot)\) n/a 124 2
35.17.l \(\chi_{35}(2, \cdot)\) n/a 248 4

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{17}^{\mathrm{old}}(\Gamma_1(35))\) into lower level spaces

\( S_{17}^{\mathrm{old}}(\Gamma_1(35)) \cong \) \(S_{17}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{17}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)