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Properties

Label 35.23
Level 35
Weight 23
Dimension 910
Nonzero newspaces 6
Sturm bound 2208
Trace bound 1

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Defining parameters

Level: \( N \) = \( 35 = 5 \cdot 7 \)
Weight: \( k \) = \( 23 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(2208\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{23}(\Gamma_1(35))\).

Total New Old
Modular forms 1080 938 142
Cusp forms 1032 910 122
Eisenstein series 48 28 20

Trace form

\( 910 q + 4094 q^{2} + 286488 q^{3} + 16777210 q^{4} + 46650938 q^{5} - 1178125704 q^{6} - 6616893418 q^{7} + 76070219502 q^{8} - 26562038958 q^{9} + O(q^{10}) \) \( 910 q + 4094 q^{2} + 286488 q^{3} + 16777210 q^{4} + 46650938 q^{5} - 1178125704 q^{6} - 6616893418 q^{7} + 76070219502 q^{8} - 26562038958 q^{9} + 238180325588 q^{10} + 393946770568 q^{11} - 4952650201812 q^{12} - 108539506612 q^{13} - 16684998277134 q^{14} + 30401685084156 q^{15} + 122087018468038 q^{16} - 103894998659272 q^{17} + 589659160270542 q^{18} - 813078042625584 q^{19} + 562120034664588 q^{20} - 1673716339685940 q^{21} + 1954861330689460 q^{22} + 599711324455532 q^{23} - 4053336729756444 q^{24} + 14806243482738136 q^{25} - 26965106857136720 q^{26} + 19822543247097240 q^{27} + 72977476593315346 q^{28} - 62995068953530212 q^{29} + 158449819481700516 q^{30} + 307839351199095868 q^{31} - 855096979998266158 q^{32} + 602098718905081908 q^{33} - 544379882253881798 q^{35} + 2243054359283666310 q^{36} + 532107966126909736 q^{37} - 770425946997187164 q^{38} + 912784164542508480 q^{39} + 344152254314803356 q^{40} + 654055225615975648 q^{41} + 4049029157835777732 q^{42} - 2905164801761769356 q^{43} - 17817760830809248488 q^{44} + 1187473765503930972 q^{45} + 23621680952106174196 q^{46} - 9747470751030066268 q^{47} - 32074453705511824044 q^{48} + 21814131162004867394 q^{49} + 30319481715285917306 q^{50} - 86496488451433376748 q^{51} + 102548800180336143020 q^{52} + 2974333597287374300 q^{53} - 219815056398288546444 q^{54} + 94615819650622745524 q^{55} + 46032071014756498854 q^{56} + 19799987577597959232 q^{57} - 217857842208289366080 q^{58} - 31157895334833533712 q^{59} + 739879599688112011608 q^{60} + 49830881761388230132 q^{61} - 759992497051409061656 q^{62} - 137658560599229190810 q^{63} + 614698514775689169814 q^{64} + 635563847390961458396 q^{65} - 2336382570232614950496 q^{66} + 288472815684857707596 q^{67} + 2406455020322315235928 q^{68} - 3867327328760744246472 q^{70} + 2463126198997039558012 q^{71} + 3854373790689721818894 q^{72} - 3076356276934854712936 q^{73} - 2608328518875550795548 q^{74} + 3321502145540010338442 q^{75} + 391190574723957296088 q^{76} - 3103123784415349954612 q^{77} - 6999053610647056928760 q^{78} - 524214417094700902364 q^{79} + 5596169944550543573432 q^{80} + 18159393608019115015746 q^{81} - 18272510883235870885172 q^{82} - 17211113990329203732484 q^{83} + 6084268583892086793564 q^{84} + 31476686455192577369948 q^{85} + 12516569176769164338196 q^{86} - 31298137323358563160392 q^{87} - 66477408720726213851184 q^{88} + 24571163222367334481340 q^{89} + 65787699802710322096200 q^{90} + 11805200863223308541216 q^{91} - 6650341984047739420156 q^{92} - 125377558298806203404028 q^{93} + 41606078292561890943444 q^{94} + 50551987590698311478442 q^{95} + 15087249769355067174600 q^{96} + 4656456708284692337492 q^{97} + 10695605096138793940686 q^{98} + 4390424411369864130420 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{23}^{\mathrm{new}}(\Gamma_1(35))\)

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
35.23.c \(\chi_{35}(34, \cdot)\) 35.23.c.a 1 1
35.23.c.b 1
35.23.c.c 84
35.23.d \(\chi_{35}(6, \cdot)\) 35.23.d.a 60 1
35.23.g \(\chi_{35}(8, \cdot)\) n/a 132 2
35.23.h \(\chi_{35}(26, \cdot)\) n/a 116 2
35.23.i \(\chi_{35}(19, \cdot)\) n/a 172 2
35.23.l \(\chi_{35}(2, \cdot)\) n/a 344 4

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

Decomposition of \(S_{23}^{\mathrm{old}}(\Gamma_1(35))\) into lower level spaces

\( S_{23}^{\mathrm{old}}(\Gamma_1(35)) \cong \) \(S_{23}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{23}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)