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Properties

Label 240.10
Level 240
Weight 10
Dimension 5318
Nonzero newspaces 14
Sturm bound 30720
Trace bound 13

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Defining parameters

Level: \( N \) = \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 14 \)
Sturm bound: \(30720\)
Trace bound: \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(240))\).

Total New Old
Modular forms 14048 5374 8674
Cusp forms 13600 5318 8282
Eisenstein series 448 56 392

Trace form

\( 5318 q - 164 q^{3} + 672 q^{4} - 718 q^{5} - 4392 q^{6} + 7556 q^{7} - 2856 q^{8} - 201318 q^{9} + O(q^{10}) \) \( 5318 q - 164 q^{3} + 672 q^{4} - 718 q^{5} - 4392 q^{6} + 7556 q^{7} - 2856 q^{8} - 201318 q^{9} + 9360 q^{10} + 395160 q^{11} + 434312 q^{12} - 711576 q^{13} - 538248 q^{14} + 627216 q^{15} - 1132224 q^{16} - 611988 q^{17} - 1232680 q^{18} - 170456 q^{19} - 1810000 q^{20} + 712884 q^{21} - 6611584 q^{22} - 3465976 q^{23} - 9200864 q^{24} - 7273778 q^{25} + 2105960 q^{26} + 11060176 q^{27} + 19694320 q^{28} + 860076 q^{29} - 775620 q^{30} - 35687112 q^{31} - 80762960 q^{32} + 21095396 q^{33} + 101271392 q^{34} + 34842192 q^{35} + 36446080 q^{36} + 12513280 q^{37} - 154184736 q^{38} - 182231876 q^{39} - 281791352 q^{40} - 18022996 q^{41} + 94382320 q^{42} + 34914132 q^{43} - 106087328 q^{44} + 42622426 q^{45} + 176329824 q^{46} + 108755688 q^{47} + 10867576 q^{48} - 665644534 q^{49} + 137252288 q^{50} + 216702288 q^{51} + 227485648 q^{52} - 613040972 q^{53} + 206632848 q^{54} + 158554688 q^{55} + 658162176 q^{56} + 81611828 q^{57} + 1226714976 q^{58} + 214654792 q^{59} - 866380832 q^{60} - 1254270196 q^{61} - 1235359992 q^{62} - 218876416 q^{63} + 68623776 q^{64} + 582411556 q^{65} + 1693075096 q^{66} - 246240676 q^{67} + 2111202288 q^{68} - 900061936 q^{69} + 821208200 q^{70} + 1470450288 q^{71} - 2568692632 q^{72} - 1774559320 q^{73} - 4354379016 q^{74} + 1860554128 q^{75} + 4039270144 q^{76} + 822324784 q^{77} + 7099311184 q^{78} - 3028854568 q^{79} + 2116199192 q^{80} + 4366131982 q^{81} - 6546527200 q^{82} + 2329133848 q^{83} - 1799917376 q^{84} + 3912691448 q^{85} - 2789067296 q^{86} + 1862992312 q^{87} + 6124438176 q^{88} + 1525554004 q^{89} + 4999258760 q^{90} - 10741512408 q^{91} + 2020722416 q^{92} - 4953107112 q^{93} - 3024072400 q^{94} + 4226484464 q^{95} - 8351074016 q^{96} + 2457492920 q^{97} - 1605541504 q^{98} - 513862224 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(240))\)

We only show spaces with even 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
240.10.a \(\chi_{240}(1, \cdot)\) 240.10.a.a 1 1
240.10.a.b 1
240.10.a.c 1
240.10.a.d 1
240.10.a.e 1
240.10.a.f 1
240.10.a.g 1
240.10.a.h 1
240.10.a.i 1
240.10.a.j 1
240.10.a.k 2
240.10.a.l 2
240.10.a.m 2
240.10.a.n 2
240.10.a.o 2
240.10.a.p 2
240.10.a.q 2
240.10.a.r 2
240.10.a.s 2
240.10.a.t 2
240.10.a.u 3
240.10.a.v 3
240.10.b \(\chi_{240}(71, \cdot)\) None 0 1
240.10.d \(\chi_{240}(169, \cdot)\) None 0 1
240.10.f \(\chi_{240}(49, \cdot)\) 240.10.f.a 4 1
240.10.f.b 6
240.10.f.c 8
240.10.f.d 10
240.10.f.e 12
240.10.f.f 14
240.10.h \(\chi_{240}(191, \cdot)\) 240.10.h.a 24 1
240.10.h.b 48
240.10.k \(\chi_{240}(121, \cdot)\) None 0 1
240.10.m \(\chi_{240}(119, \cdot)\) None 0 1
240.10.o \(\chi_{240}(239, \cdot)\) n/a 108 1
240.10.s \(\chi_{240}(61, \cdot)\) n/a 288 2
240.10.t \(\chi_{240}(59, \cdot)\) n/a 856 2
240.10.v \(\chi_{240}(17, \cdot)\) n/a 212 2
240.10.w \(\chi_{240}(127, \cdot)\) n/a 108 2
240.10.y \(\chi_{240}(163, \cdot)\) n/a 432 2
240.10.bb \(\chi_{240}(173, \cdot)\) n/a 856 2
240.10.bc \(\chi_{240}(43, \cdot)\) n/a 432 2
240.10.bf \(\chi_{240}(53, \cdot)\) n/a 856 2
240.10.bh \(\chi_{240}(7, \cdot)\) None 0 2
240.10.bi \(\chi_{240}(137, \cdot)\) None 0 2
240.10.bk \(\chi_{240}(11, \cdot)\) n/a 576 2
240.10.bl \(\chi_{240}(109, \cdot)\) n/a 432 2

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

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(240))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(240)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 10}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 5}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 2}\)