Properties

Label 240.3
Level 240
Weight 3
Dimension 1162
Nonzero newspaces 14
Newform subspaces 31
Sturm bound 9216
Trace bound 4

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Defining parameters

Level: \( N \) = \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 14 \)
Newform subspaces: \( 31 \)
Sturm bound: \(9216\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(240))\).

Total New Old
Modular forms 3296 1214 2082
Cusp forms 2848 1162 1686
Eisenstein series 448 52 396

Trace form

\( 1162 q - 4 q^{3} - 32 q^{4} - 12 q^{5} - 24 q^{6} - 32 q^{7} + 24 q^{8} + 18 q^{9} + O(q^{10}) \) \( 1162 q - 4 q^{3} - 32 q^{4} - 12 q^{5} - 24 q^{6} - 32 q^{7} + 24 q^{8} + 18 q^{9} + 64 q^{10} - 64 q^{11} + 104 q^{12} + 88 q^{14} - 18 q^{15} - 64 q^{16} - 8 q^{17} + 88 q^{18} + 188 q^{19} - 80 q^{20} + 64 q^{21} - 160 q^{22} + 352 q^{23} + 32 q^{24} + 34 q^{25} + 200 q^{26} + 44 q^{27} + 240 q^{28} + 56 q^{29} + 124 q^{30} - 60 q^{31} + 240 q^{32} - 8 q^{33} + 160 q^{34} - 384 q^{36} + 208 q^{37} - 224 q^{38} + 176 q^{39} - 312 q^{40} + 88 q^{41} - 688 q^{42} - 40 q^{43} - 736 q^{44} - 32 q^{45} - 800 q^{46} - 192 q^{47} - 520 q^{48} - 694 q^{49} - 544 q^{50} - 172 q^{51} - 112 q^{52} + 168 q^{53} + 320 q^{54} + 80 q^{55} + 448 q^{56} + 144 q^{57} + 832 q^{58} + 256 q^{59} + 512 q^{60} + 572 q^{61} + 552 q^{62} + 160 q^{63} + 544 q^{64} + 312 q^{65} + 152 q^{66} + 792 q^{67} - 336 q^{68} - 36 q^{69} - 1240 q^{70} + 256 q^{71} - 344 q^{72} - 616 q^{73} - 1576 q^{74} - 72 q^{75} - 2112 q^{76} - 928 q^{77} - 1456 q^{78} - 764 q^{79} - 392 q^{80} - 38 q^{81} - 992 q^{82} - 864 q^{83} - 1152 q^{84} - 1148 q^{85} - 160 q^{86} - 1240 q^{87} - 96 q^{88} - 696 q^{89} + 328 q^{90} - 2656 q^{91} + 880 q^{92} - 464 q^{93} + 1712 q^{94} - 2112 q^{95} + 1056 q^{96} - 56 q^{97} + 1792 q^{98} - 456 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(240))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
240.3.c \(\chi_{240}(209, \cdot)\) 240.3.c.a 1 1
240.3.c.b 1
240.3.c.c 4
240.3.c.d 4
240.3.c.e 12
240.3.e \(\chi_{240}(31, \cdot)\) 240.3.e.a 4 1
240.3.e.b 4
240.3.g \(\chi_{240}(151, \cdot)\) None 0 1
240.3.i \(\chi_{240}(89, \cdot)\) None 0 1
240.3.j \(\chi_{240}(79, \cdot)\) 240.3.j.a 4 1
240.3.j.b 4
240.3.j.c 4
240.3.l \(\chi_{240}(161, \cdot)\) 240.3.l.a 2 1
240.3.l.b 2
240.3.l.c 4
240.3.l.d 8
240.3.n \(\chi_{240}(41, \cdot)\) None 0 1
240.3.p \(\chi_{240}(199, \cdot)\) None 0 1
240.3.q \(\chi_{240}(19, \cdot)\) 240.3.q.a 96 2
240.3.r \(\chi_{240}(101, \cdot)\) 240.3.r.a 128 2
240.3.u \(\chi_{240}(23, \cdot)\) None 0 2
240.3.x \(\chi_{240}(73, \cdot)\) None 0 2
240.3.z \(\chi_{240}(83, \cdot)\) 240.3.z.a 184 2
240.3.ba \(\chi_{240}(13, \cdot)\) 240.3.ba.a 96 2
240.3.bd \(\chi_{240}(203, \cdot)\) 240.3.bd.a 184 2
240.3.be \(\chi_{240}(133, \cdot)\) 240.3.be.a 96 2
240.3.bg \(\chi_{240}(97, \cdot)\) 240.3.bg.a 4 2
240.3.bg.b 4
240.3.bg.c 4
240.3.bg.d 4
240.3.bg.e 8
240.3.bj \(\chi_{240}(47, \cdot)\) 240.3.bj.a 8 2
240.3.bj.b 16
240.3.bj.c 24
240.3.bm \(\chi_{240}(29, \cdot)\) 240.3.bm.a 8 2
240.3.bm.b 176
240.3.bn \(\chi_{240}(91, \cdot)\) 240.3.bn.a 64 2

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(240))\) into lower level spaces

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