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Properties

Label 272.4
Level 272
Weight 4
Dimension 3794
Nonzero newspaces 13
Sturm bound 18432
Trace bound 6

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Defining parameters

Level: \( N \) = \( 272 = 2^{4} \cdot 17 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 13 \)
Sturm bound: \(18432\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(272))\).

Total New Old
Modular forms 7136 3928 3208
Cusp forms 6688 3794 2894
Eisenstein series 448 134 314

Trace form

\( 3794 q - 28 q^{2} - 28 q^{3} - 48 q^{4} - 32 q^{5} + 32 q^{6} + 24 q^{7} + 56 q^{8} + 14 q^{9} + O(q^{10}) \) \( 3794 q - 28 q^{2} - 28 q^{3} - 48 q^{4} - 32 q^{5} + 32 q^{6} + 24 q^{7} + 56 q^{8} + 14 q^{9} + 104 q^{10} - 148 q^{11} - 232 q^{12} - 80 q^{13} - 408 q^{14} + 240 q^{15} - 592 q^{16} - 118 q^{17} - 412 q^{18} + 116 q^{19} + 360 q^{20} + 48 q^{21} + 1144 q^{22} - 136 q^{23} + 1664 q^{24} + 234 q^{25} + 496 q^{26} - 88 q^{27} - 592 q^{28} - 32 q^{29} - 2504 q^{30} - 1080 q^{31} - 1968 q^{32} - 424 q^{33} - 468 q^{34} - 1096 q^{35} + 1160 q^{36} + 304 q^{37} + 2432 q^{38} - 200 q^{39} + 2640 q^{40} + 388 q^{41} + 1328 q^{42} + 1756 q^{43} - 1768 q^{44} - 472 q^{45} - 2296 q^{46} + 2920 q^{47} - 3568 q^{48} - 726 q^{49} - 1484 q^{50} + 1276 q^{51} + 408 q^{52} - 1088 q^{53} + 2720 q^{54} - 4120 q^{55} + 944 q^{56} - 2408 q^{57} - 48 q^{58} - 5012 q^{59} + 352 q^{60} - 1360 q^{61} + 128 q^{62} + 960 q^{63} - 1056 q^{64} + 4904 q^{65} + 824 q^{66} - 308 q^{67} + 848 q^{68} + 6632 q^{69} - 352 q^{70} + 4072 q^{71} - 2216 q^{72} + 2052 q^{73} + 872 q^{74} + 8436 q^{75} + 2424 q^{76} + 1136 q^{77} + 1512 q^{78} + 4376 q^{79} + 5264 q^{80} - 7774 q^{81} + 1376 q^{82} - 2732 q^{83} - 3952 q^{84} - 3752 q^{85} - 7592 q^{86} - 1608 q^{87} - 3088 q^{88} - 1436 q^{89} - 3824 q^{90} - 5632 q^{91} - 1296 q^{92} + 3064 q^{93} + 6464 q^{94} - 14000 q^{95} + 8832 q^{96} + 892 q^{97} - 660 q^{98} - 8756 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(272))\)

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
272.4.a \(\chi_{272}(1, \cdot)\) 272.4.a.a 1 1
272.4.a.b 1
272.4.a.c 1
272.4.a.d 1
272.4.a.e 2
272.4.a.f 2
272.4.a.g 3
272.4.a.h 3
272.4.a.i 3
272.4.a.j 3
272.4.a.k 4
272.4.b \(\chi_{272}(33, \cdot)\) 272.4.b.a 2 1
272.4.b.b 2
272.4.b.c 4
272.4.b.d 4
272.4.b.e 6
272.4.b.f 8
272.4.c \(\chi_{272}(137, \cdot)\) None 0 1
272.4.h \(\chi_{272}(169, \cdot)\) None 0 1
272.4.j \(\chi_{272}(13, \cdot)\) n/a 212 2
272.4.l \(\chi_{272}(69, \cdot)\) n/a 192 2
272.4.m \(\chi_{272}(89, \cdot)\) None 0 2
272.4.o \(\chi_{272}(81, \cdot)\) 272.4.o.a 2 2
272.4.o.b 2
272.4.o.c 6
272.4.o.d 6
272.4.o.e 8
272.4.o.f 14
272.4.o.g 14
272.4.r \(\chi_{272}(101, \cdot)\) n/a 212 2
272.4.s \(\chi_{272}(149, \cdot)\) n/a 212 2
272.4.v \(\chi_{272}(49, \cdot)\) n/a 104 4
272.4.w \(\chi_{272}(189, \cdot)\) n/a 424 4
272.4.y \(\chi_{272}(53, \cdot)\) n/a 424 4
272.4.ba \(\chi_{272}(9, \cdot)\) None 0 4
272.4.bd \(\chi_{272}(3, \cdot)\) n/a 848 8
272.4.bf \(\chi_{272}(31, \cdot)\) n/a 216 8
272.4.bg \(\chi_{272}(7, \cdot)\) None 0 8
272.4.bj \(\chi_{272}(107, \cdot)\) n/a 848 8

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(272))\) into lower level spaces

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