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Properties

Label 272.3
Level 272
Weight 3
Dimension 2506
Nonzero newspaces 13
Newform subspaces 28
Sturm bound 13824
Trace bound 6

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Defining parameters

Level: \( N \) = \( 272 = 2^{4} \cdot 17 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 13 \)
Newform subspaces: \( 28 \)
Sturm bound: \(13824\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(272))\).

Total New Old
Modular forms 4832 2642 2190
Cusp forms 4384 2506 1878
Eisenstein series 448 136 312

Trace form

\( 2506 q - 28 q^{2} - 20 q^{3} - 16 q^{4} - 24 q^{5} - 16 q^{6} - 16 q^{7} - 40 q^{8} - 26 q^{9} + O(q^{10}) \) \( 2506 q - 28 q^{2} - 20 q^{3} - 16 q^{4} - 24 q^{5} - 16 q^{6} - 16 q^{7} - 40 q^{8} - 26 q^{9} - 104 q^{10} + 12 q^{11} - 136 q^{12} - 56 q^{13} - 56 q^{14} - 24 q^{15} + 48 q^{16} - 38 q^{17} + 84 q^{18} - 84 q^{19} + 136 q^{20} + 72 q^{22} - 144 q^{23} - 128 q^{24} - 30 q^{25} - 224 q^{26} - 152 q^{27} - 144 q^{28} - 88 q^{29} - 136 q^{30} - 24 q^{31} - 48 q^{32} - 56 q^{33} + 44 q^{34} + 152 q^{35} + 72 q^{36} + 8 q^{37} - 112 q^{38} + 368 q^{39} - 112 q^{40} - 44 q^{41} + 16 q^{42} + 204 q^{43} - 72 q^{44} - 64 q^{45} - 88 q^{46} - 24 q^{47} + 16 q^{48} - 78 q^{49} - 124 q^{50} - 180 q^{51} - 264 q^{52} - 152 q^{53} - 96 q^{54} + 48 q^{55} + 304 q^{56} + 632 q^{57} + 320 q^{58} - 52 q^{59} + 288 q^{60} + 328 q^{61} + 256 q^{62} + 552 q^{63} - 160 q^{64} + 152 q^{65} - 424 q^{66} + 420 q^{67} - 144 q^{68} - 104 q^{69} + 304 q^{71} - 136 q^{72} - 172 q^{73} + 152 q^{74} - 700 q^{75} + 344 q^{76} - 256 q^{77} + 136 q^{78} - 600 q^{79} - 496 q^{80} - 1302 q^{81} - 640 q^{82} - 1428 q^{83} - 496 q^{84} - 296 q^{85} - 600 q^{86} - 912 q^{87} - 16 q^{88} + 148 q^{89} + 288 q^{90} - 400 q^{91} + 304 q^{92} + 24 q^{93} - 128 q^{94} - 24 q^{95} + 128 q^{96} - 324 q^{97} - 52 q^{98} + 356 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(272))\)

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
272.3.d \(\chi_{272}(239, \cdot)\) 272.3.d.a 4 1
272.3.d.b 12
272.3.e \(\chi_{272}(135, \cdot)\) None 0 1
272.3.f \(\chi_{272}(103, \cdot)\) None 0 1
272.3.g \(\chi_{272}(271, \cdot)\) 272.3.g.a 2 1
272.3.g.b 2
272.3.g.c 2
272.3.g.d 12
272.3.i \(\chi_{272}(251, \cdot)\) 272.3.i.a 140 2
272.3.k \(\chi_{272}(67, \cdot)\) 272.3.k.a 140 2
272.3.n \(\chi_{272}(55, \cdot)\) None 0 2
272.3.p \(\chi_{272}(47, \cdot)\) 272.3.p.a 2 2
272.3.p.b 2
272.3.p.c 4
272.3.p.d 4
272.3.p.e 24
272.3.q \(\chi_{272}(35, \cdot)\) 272.3.q.a 128 2
272.3.t \(\chi_{272}(115, \cdot)\) 272.3.t.a 140 2
272.3.u \(\chi_{272}(15, \cdot)\) 272.3.u.a 24 4
272.3.u.b 48
272.3.x \(\chi_{272}(155, \cdot)\) 272.3.x.a 280 4
272.3.z \(\chi_{272}(19, \cdot)\) 272.3.z.a 280 4
272.3.bb \(\chi_{272}(87, \cdot)\) None 0 4
272.3.bc \(\chi_{272}(29, \cdot)\) 272.3.bc.a 560 8
272.3.be \(\chi_{272}(41, \cdot)\) None 0 8
272.3.bh \(\chi_{272}(65, \cdot)\) 272.3.bh.a 8 8
272.3.bh.b 8
272.3.bh.c 8
272.3.bh.d 16
272.3.bh.e 24
272.3.bh.f 32
272.3.bh.g 40
272.3.bi \(\chi_{272}(5, \cdot)\) 272.3.bi.a 560 8

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(272))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(272)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(272))\)\(^{\oplus 1}\)