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Properties

Label 240.5
Level 240
Weight 5
Dimension 2350
Nonzero newspaces 14
Sturm bound 15360
Trace bound 4

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Defining parameters

Level: \( N \) = \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 14 \)
Sturm bound: \(15360\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(240))\).

Total New Old
Modular forms 6368 2402 3966
Cusp forms 5920 2350 3570
Eisenstein series 448 52 396

Trace form

\( 2350 q - 4 q^{3} - 32 q^{4} + 72 q^{5} + 120 q^{6} - 48 q^{7} - 360 q^{8} + 102 q^{9} + O(q^{10}) \) \( 2350 q - 4 q^{3} - 32 q^{4} + 72 q^{5} + 120 q^{6} - 48 q^{7} - 360 q^{8} + 102 q^{9} - 208 q^{10} + 384 q^{11} - 664 q^{12} + 584 q^{13} + 312 q^{14} + 414 q^{15} + 1216 q^{16} + 240 q^{17} - 392 q^{18} - 2692 q^{19} + 1200 q^{20} - 2288 q^{21} + 1536 q^{22} + 1728 q^{23} - 736 q^{24} - 3578 q^{25} - 5400 q^{26} - 1828 q^{27} - 3600 q^{28} + 8496 q^{29} + 4396 q^{30} + 5268 q^{31} - 1680 q^{32} - 2312 q^{33} - 6816 q^{34} + 384 q^{36} - 16664 q^{37} + 3360 q^{38} - 7456 q^{39} + 9288 q^{40} + 4656 q^{41} + 7472 q^{42} - 11592 q^{43} - 2400 q^{44} + 4708 q^{45} + 23328 q^{46} + 5760 q^{47} + 12536 q^{48} + 18990 q^{49} - 96 q^{50} + 24500 q^{51} + 2448 q^{52} + 2832 q^{53} - 14128 q^{54} - 5584 q^{55} - 30912 q^{56} - 2784 q^{57} - 34208 q^{58} - 26112 q^{59} - 13696 q^{60} - 36268 q^{61} - 43704 q^{62} - 9920 q^{63} - 86240 q^{64} - 10896 q^{65} - 34696 q^{66} + 10040 q^{67} + 53040 q^{68} + 21948 q^{69} + 93704 q^{70} - 19968 q^{71} + 54568 q^{72} - 2384 q^{73} + 59832 q^{74} - 49416 q^{75} + 80832 q^{76} + 7104 q^{77} + 31088 q^{78} + 2324 q^{79} - 11208 q^{80} + 56398 q^{81} + 52320 q^{82} + 37440 q^{83} - 12672 q^{84} - 164 q^{85} - 107808 q^{86} + 68696 q^{87} - 173152 q^{88} - 19440 q^{89} - 44024 q^{90} + 30048 q^{91} - 4752 q^{92} - 32288 q^{93} + 81584 q^{94} - 93312 q^{95} + 91680 q^{96} + 44448 q^{97} + 44544 q^{98} + 8568 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(240))\)

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
240.5.c \(\chi_{240}(209, \cdot)\) 240.5.c.a 1 1
240.5.c.b 1
240.5.c.c 4
240.5.c.d 8
240.5.c.e 8
240.5.c.f 24
240.5.e \(\chi_{240}(31, \cdot)\) 240.5.e.a 4 1
240.5.e.b 4
240.5.e.c 8
240.5.g \(\chi_{240}(151, \cdot)\) None 0 1
240.5.i \(\chi_{240}(89, \cdot)\) None 0 1
240.5.j \(\chi_{240}(79, \cdot)\) 240.5.j.a 8 1
240.5.j.b 16
240.5.l \(\chi_{240}(161, \cdot)\) 240.5.l.a 2 1
240.5.l.b 4
240.5.l.c 4
240.5.l.d 6
240.5.l.e 16
240.5.n \(\chi_{240}(41, \cdot)\) None 0 1
240.5.p \(\chi_{240}(199, \cdot)\) None 0 1
240.5.q \(\chi_{240}(19, \cdot)\) n/a 192 2
240.5.r \(\chi_{240}(101, \cdot)\) n/a 256 2
240.5.u \(\chi_{240}(23, \cdot)\) None 0 2
240.5.x \(\chi_{240}(73, \cdot)\) None 0 2
240.5.z \(\chi_{240}(83, \cdot)\) n/a 376 2
240.5.ba \(\chi_{240}(13, \cdot)\) n/a 192 2
240.5.bd \(\chi_{240}(203, \cdot)\) n/a 376 2
240.5.be \(\chi_{240}(133, \cdot)\) n/a 192 2
240.5.bg \(\chi_{240}(97, \cdot)\) 240.5.bg.a 4 2
240.5.bg.b 4
240.5.bg.c 8
240.5.bg.d 8
240.5.bg.e 12
240.5.bg.f 12
240.5.bj \(\chi_{240}(47, \cdot)\) 240.5.bj.a 32 2
240.5.bj.b 64
240.5.bm \(\chi_{240}(29, \cdot)\) n/a 376 2
240.5.bn \(\chi_{240}(91, \cdot)\) n/a 128 2

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(240))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(240)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 10}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 5}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 1}\)