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Properties

Label 270.6
Level 270
Weight 6
Dimension 2348
Nonzero newspaces 9
Sturm bound 23328
Trace bound 2

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Defining parameters

Level: \( N \) = \( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 9 \)
Sturm bound: \(23328\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(270))\).

Total New Old
Modular forms 9960 2348 7612
Cusp forms 9480 2348 7132
Eisenstein series 480 0 480

Trace form

\( 2348 q - 8 q^{2} - 32 q^{4} - 282 q^{5} - 240 q^{6} + 344 q^{7} + 640 q^{8} + 1320 q^{9} + O(q^{10}) \) \( 2348 q - 8 q^{2} - 32 q^{4} - 282 q^{5} - 240 q^{6} + 344 q^{7} + 640 q^{8} + 1320 q^{9} - 776 q^{10} - 3212 q^{11} - 1056 q^{12} - 5708 q^{13} + 1248 q^{14} + 3258 q^{15} - 512 q^{16} + 12564 q^{17} - 11568 q^{18} - 5732 q^{19} + 128 q^{20} + 29184 q^{21} - 4256 q^{22} - 30972 q^{23} + 9066 q^{25} - 19072 q^{26} - 35262 q^{27} - 64 q^{28} - 19848 q^{29} + 10224 q^{30} - 25112 q^{31} - 2048 q^{32} + 57234 q^{33} - 34960 q^{34} + 84138 q^{35} + 6336 q^{36} + 44224 q^{37} + 23240 q^{38} + 44460 q^{39} + 5504 q^{40} - 116540 q^{41} - 61248 q^{42} - 162392 q^{43} - 29056 q^{44} - 88356 q^{45} - 4800 q^{46} + 98748 q^{47} - 3072 q^{48} + 135534 q^{49} + 226488 q^{50} - 94416 q^{51} - 22976 q^{52} - 191904 q^{53} - 2592 q^{54} - 23302 q^{55} - 17408 q^{56} - 130518 q^{57} - 45808 q^{58} + 219886 q^{59} + 52128 q^{60} + 63492 q^{61} + 344864 q^{62} + 672636 q^{63} + 237568 q^{64} - 165022 q^{65} - 120960 q^{66} + 16220 q^{67} - 99360 q^{68} + 42516 q^{69} + 126952 q^{70} - 105408 q^{71} + 218112 q^{72} - 488724 q^{73} - 69168 q^{74} - 111984 q^{75} + 42144 q^{76} + 594984 q^{77} - 214560 q^{78} - 209504 q^{79} - 21504 q^{80} - 80880 q^{81} - 88304 q^{82} - 420792 q^{83} - 172800 q^{84} - 956016 q^{85} - 1038320 q^{86} - 413472 q^{87} + 204928 q^{88} - 1087618 q^{89} + 274680 q^{90} - 337660 q^{91} + 244608 q^{92} + 955380 q^{93} + 778672 q^{94} + 512978 q^{95} - 12288 q^{96} + 536512 q^{97} + 1402824 q^{98} + 564576 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(270))\)

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
270.6.a \(\chi_{270}(1, \cdot)\) 270.6.a.a 1 1
270.6.a.b 1
270.6.a.c 1
270.6.a.d 1
270.6.a.e 2
270.6.a.f 2
270.6.a.g 2
270.6.a.h 2
270.6.a.i 2
270.6.a.j 2
270.6.a.k 2
270.6.a.l 2
270.6.a.m 2
270.6.a.n 2
270.6.a.o 2
270.6.a.p 2
270.6.c \(\chi_{270}(109, \cdot)\) 270.6.c.a 8 1
270.6.c.b 10
270.6.c.c 10
270.6.c.d 12
270.6.e \(\chi_{270}(91, \cdot)\) 270.6.e.a 8 2
270.6.e.b 10
270.6.e.c 10
270.6.e.d 12
270.6.f \(\chi_{270}(53, \cdot)\) 270.6.f.a 40 2
270.6.f.b 40
270.6.i \(\chi_{270}(19, \cdot)\) 270.6.i.a 60 2
270.6.k \(\chi_{270}(31, \cdot)\) n/a 360 6
270.6.m \(\chi_{270}(17, \cdot)\) n/a 120 4
270.6.p \(\chi_{270}(49, \cdot)\) n/a 540 6
270.6.r \(\chi_{270}(23, \cdot)\) n/a 1080 12

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(270))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(270)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 2}\)