↑

Properties

Label 35.15
Level 35
Weight 15
Dimension 574
Nonzero newspaces 6
Sturm bound 1440
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 35 = 5 \cdot 7 \)
Weight: \( k \) = \( 15 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(1440\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{15}(\Gamma_1(35))\).

Total New Old
Modular forms 696 602 94
Cusp forms 648 574 74
Eisenstein series 48 28 20

Trace form

\( 574 q + 254 q^{2} - 60 q^{3} - 65542 q^{4} - 32812 q^{5} - 613512 q^{6} + 2817026 q^{7} - 25612626 q^{8} + 31013442 q^{9} + O(q^{10}) \) \( 574 q + 254 q^{2} - 60 q^{3} - 65542 q^{4} - 32812 q^{5} - 613512 q^{6} + 2817026 q^{7} - 25612626 q^{8} + 31013442 q^{9} + 3269268 q^{10} - 23338604 q^{11} - 18308628 q^{12} - 111276372 q^{13} + 400788978 q^{14} - 503626104 q^{15} - 629495354 q^{16} + 971791532 q^{17} + 3140617998 q^{18} - 3851108364 q^{19} - 956120052 q^{20} + 20231340168 q^{21} - 20975037708 q^{22} - 24531617056 q^{23} + 20594441124 q^{24} + 29535278446 q^{25} + 6575595376 q^{26} - 106590945360 q^{27} + 82346939986 q^{28} + 126311129772 q^{29} - 58037988924 q^{30} + 20107670256 q^{31} - 300018708718 q^{32} + 319618504992 q^{33} - 294707299088 q^{35} + 702558699078 q^{36} + 49308863404 q^{37} - 1207600438044 q^{38} - 291077392008 q^{39} + 2039064499836 q^{40} - 533018923808 q^{41} + 97369930308 q^{42} - 371463210884 q^{43} + 638633450520 q^{44} + 2379735868632 q^{45} + 252081652212 q^{46} - 4514281643656 q^{47} - 9904297548204 q^{48} + 6226970589058 q^{49} + 3367377935546 q^{50} + 8084063113320 q^{51} - 9988764616404 q^{52} - 4632573453352 q^{53} - 16734078588108 q^{54} - 8239912948476 q^{55} + 38683982540838 q^{56} + 32012983223688 q^{57} - 11148959952192 q^{58} - 22516049132508 q^{59} - 16787770941192 q^{60} + 361716871704 q^{61} + 35693779568104 q^{62} + 14596291387458 q^{63} + 25178176952342 q^{64} - 37663197064204 q^{65} - 91505161039392 q^{66} - 531123100432 q^{67} + 87314656246744 q^{68} - 103493817565512 q^{70} - 18865592838164 q^{71} + 116960852324622 q^{72} + 32936168576460 q^{73} - 121088418527388 q^{74} - 88379080840308 q^{75} + 139025461515480 q^{76} + 266471647208816 q^{77} + 199173612754824 q^{78} - 133241880144352 q^{79} - 302380399926088 q^{80} - 404466148994514 q^{81} + 50567300358924 q^{82} + 148668022098836 q^{83} + 541023403736412 q^{84} + 99559283145168 q^{85} + 292834008014164 q^{86} - 258620251570728 q^{87} - 830998670879280 q^{88} - 470130680225592 q^{89} - 155658357940920 q^{90} + 200616868723416 q^{91} + 564217090630532 q^{92} + 890417929383744 q^{93} + 126864218552340 q^{94} + 23215765960092 q^{95} - 1034785731157944 q^{96} - 1355840805993708 q^{97} - 648471356726706 q^{98} + 1265802071093268 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{15}^{\mathrm{new}}(\Gamma_1(35))\)

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
35.15.c \(\chi_{35}(34, \cdot)\) 35.15.c.a 1 1
35.15.c.b 1
35.15.c.c 52
35.15.d \(\chi_{35}(6, \cdot)\) 35.15.d.a 36 1
35.15.g \(\chi_{35}(8, \cdot)\) 35.15.g.a 84 2
35.15.h \(\chi_{35}(26, \cdot)\) 35.15.h.a 76 2
35.15.i \(\chi_{35}(19, \cdot)\) n/a 108 2
35.15.l \(\chi_{35}(2, \cdot)\) n/a 216 4

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

Decomposition of \(S_{15}^{\mathrm{old}}(\Gamma_1(35))\) into lower level spaces

\( S_{15}^{\mathrm{old}}(\Gamma_1(35)) \cong \) \(S_{15}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{15}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)