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Properties

Label 240.6
Level 240
Weight 6
Dimension 2942
Nonzero newspaces 14
Sturm bound 18432
Trace bound 13

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Defining parameters

Level: \( N \) = \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 14 \)
Sturm bound: \(18432\)
Trace bound: \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(240))\).

Total New Old
Modular forms 7904 2998 4906
Cusp forms 7456 2942 4514
Eisenstein series 448 56 392

Trace form

\( 2942 q - 20 q^{3} - 96 q^{4} - 38 q^{5} + 216 q^{6} + 324 q^{7} + 984 q^{8} - 942 q^{9} + O(q^{10}) \) \( 2942 q - 20 q^{3} - 96 q^{4} - 38 q^{5} + 216 q^{6} + 324 q^{7} + 984 q^{8} - 942 q^{9} - 880 q^{10} - 3624 q^{11} + 8 q^{12} + 952 q^{13} - 648 q^{14} - 624 q^{15} - 8384 q^{16} + 1212 q^{17} + 8792 q^{18} - 10712 q^{19} + 7600 q^{20} - 684 q^{21} - 2432 q^{22} + 1672 q^{23} - 15584 q^{24} - 26138 q^{25} + 25960 q^{26} + 1696 q^{27} - 12560 q^{28} - 420 q^{29} - 4740 q^{30} - 26376 q^{31} + 14000 q^{32} + 23012 q^{33} + 36192 q^{34} + 23952 q^{35} + 58240 q^{36} - 49808 q^{37} - 4896 q^{38} + 55996 q^{39} - 146552 q^{40} - 55364 q^{41} - 50960 q^{42} - 45676 q^{43} - 4768 q^{44} - 14174 q^{45} + 43360 q^{46} - 5016 q^{47} + 107896 q^{48} - 14846 q^{49} - 12992 q^{50} + 4848 q^{51} + 16080 q^{52} + 62660 q^{53} + 68112 q^{54} + 86528 q^{55} + 317184 q^{56} + 3092 q^{57} + 70752 q^{58} + 61064 q^{59} + 44128 q^{60} - 114244 q^{61} - 382200 q^{62} - 248896 q^{63} - 162912 q^{64} - 65644 q^{65} - 345320 q^{66} + 42972 q^{67} - 362256 q^{68} + 81488 q^{69} - 425080 q^{70} + 658416 q^{71} - 269464 q^{72} - 280392 q^{73} + 286968 q^{74} - 381632 q^{75} + 2560 q^{76} - 311056 q^{77} + 463312 q^{78} - 833384 q^{79} + 362392 q^{80} + 907366 q^{81} + 1067808 q^{82} - 134056 q^{83} + 220096 q^{84} + 265448 q^{85} + 798176 q^{86} + 232408 q^{87} - 65888 q^{88} - 161596 q^{89} - 1127800 q^{90} + 332456 q^{91} - 1359632 q^{92} - 812616 q^{93} - 1468624 q^{94} - 85136 q^{95} + 628000 q^{96} - 670968 q^{97} + 666496 q^{98} - 190224 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(240))\)

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
240.6.a \(\chi_{240}(1, \cdot)\) 240.6.a.a 1 1
240.6.a.b 1
240.6.a.c 1
240.6.a.d 1
240.6.a.e 1
240.6.a.f 1
240.6.a.g 1
240.6.a.h 1
240.6.a.i 1
240.6.a.j 1
240.6.a.k 1
240.6.a.l 1
240.6.a.m 1
240.6.a.n 1
240.6.a.o 2
240.6.a.p 2
240.6.a.q 2
240.6.b \(\chi_{240}(71, \cdot)\) None 0 1
240.6.d \(\chi_{240}(169, \cdot)\) None 0 1
240.6.f \(\chi_{240}(49, \cdot)\) 240.6.f.a 2 1
240.6.f.b 4
240.6.f.c 4
240.6.f.d 6
240.6.f.e 6
240.6.f.f 8
240.6.h \(\chi_{240}(191, \cdot)\) 240.6.h.a 12 1
240.6.h.b 28
240.6.k \(\chi_{240}(121, \cdot)\) None 0 1
240.6.m \(\chi_{240}(119, \cdot)\) None 0 1
240.6.o \(\chi_{240}(239, \cdot)\) 240.6.o.a 4 1
240.6.o.b 16
240.6.o.c 40
240.6.s \(\chi_{240}(61, \cdot)\) n/a 160 2
240.6.t \(\chi_{240}(59, \cdot)\) n/a 472 2
240.6.v \(\chi_{240}(17, \cdot)\) n/a 116 2
240.6.w \(\chi_{240}(127, \cdot)\) 240.6.w.a 20 2
240.6.w.b 40
240.6.y \(\chi_{240}(163, \cdot)\) n/a 240 2
240.6.bb \(\chi_{240}(173, \cdot)\) n/a 472 2
240.6.bc \(\chi_{240}(43, \cdot)\) n/a 240 2
240.6.bf \(\chi_{240}(53, \cdot)\) n/a 472 2
240.6.bh \(\chi_{240}(7, \cdot)\) None 0 2
240.6.bi \(\chi_{240}(137, \cdot)\) None 0 2
240.6.bk \(\chi_{240}(11, \cdot)\) n/a 320 2
240.6.bl \(\chi_{240}(109, \cdot)\) n/a 240 2

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(240))\) into lower level spaces

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