Properties

Label 270.3
Level 270
Weight 3
Dimension 940
Nonzero newspaces 9
Newform subspaces 21
Sturm bound 11664
Trace bound 4

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Defining parameters

Level: \( N \) = \( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 9 \)
Newform subspaces: \( 21 \)
Sturm bound: \(11664\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(270))\).

Total New Old
Modular forms 4128 940 3188
Cusp forms 3648 940 2708
Eisenstein series 480 0 480

Trace form

\( 940 q - 36 q^{5} - 24 q^{6} - 24 q^{7} + 24 q^{9} + O(q^{10}) \) \( 940 q - 36 q^{5} - 24 q^{6} - 24 q^{7} + 24 q^{9} - 8 q^{10} + 24 q^{11} + 24 q^{12} + 8 q^{13} + 144 q^{14} + 18 q^{15} + 72 q^{17} + 96 q^{18} + 44 q^{19} + 84 q^{20} + 456 q^{21} - 32 q^{22} + 372 q^{23} + 8 q^{25} - 108 q^{27} + 24 q^{28} - 252 q^{29} - 144 q^{30} + 176 q^{31} - 384 q^{33} + 272 q^{34} + 738 q^{35} - 144 q^{36} + 308 q^{37} + 216 q^{38} + 396 q^{39} + 80 q^{40} + 504 q^{41} + 96 q^{42} - 16 q^{43} + 258 q^{45} + 168 q^{47} - 48 q^{48} - 744 q^{49} - 960 q^{50} - 564 q^{51} - 304 q^{52} - 1848 q^{53} - 648 q^{54} - 628 q^{55} - 192 q^{56} - 1080 q^{57} - 400 q^{58} - 972 q^{59} - 36 q^{60} - 344 q^{61} - 288 q^{62} - 636 q^{63} - 192 q^{64} - 192 q^{65} + 864 q^{66} + 1380 q^{67} + 360 q^{68} + 1044 q^{69} + 460 q^{70} + 1248 q^{71} + 384 q^{72} + 1144 q^{73} + 1152 q^{74} + 1146 q^{75} + 520 q^{76} + 2616 q^{77} + 576 q^{78} + 848 q^{79} + 120 q^{81} - 128 q^{82} - 240 q^{83} - 432 q^{84} - 228 q^{85} - 864 q^{86} - 1884 q^{87} - 368 q^{88} - 1296 q^{89} - 720 q^{90} - 536 q^{91} - 768 q^{92} - 1500 q^{93} - 1544 q^{94} - 1848 q^{95} - 192 q^{96} - 2212 q^{97} - 1584 q^{98} - 1452 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(270))\)

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
270.3.b \(\chi_{270}(269, \cdot)\) 270.3.b.a 4 1
270.3.b.b 4
270.3.b.c 4
270.3.b.d 4
270.3.d \(\chi_{270}(161, \cdot)\) 270.3.d.a 4 1
270.3.d.b 8
270.3.g \(\chi_{270}(163, \cdot)\) 270.3.g.a 4 2
270.3.g.b 4
270.3.g.c 4
270.3.g.d 4
270.3.g.e 8
270.3.g.f 8
270.3.h \(\chi_{270}(71, \cdot)\) 270.3.h.a 16 2
270.3.j \(\chi_{270}(89, \cdot)\) 270.3.j.a 8 2
270.3.j.b 16
270.3.l \(\chi_{270}(37, \cdot)\) 270.3.l.a 24 4
270.3.l.b 24
270.3.n \(\chi_{270}(29, \cdot)\) 270.3.n.a 216 6
270.3.o \(\chi_{270}(11, \cdot)\) 270.3.o.a 144 6
270.3.q \(\chi_{270}(7, \cdot)\) 270.3.q.a 216 12
270.3.q.b 216

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(270))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(270)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 2}\)