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Properties

Label 272.2
Level 272
Weight 2
Dimension 1220
Nonzero newspaces 13
Newform subspaces 38
Sturm bound 9216
Trace bound 6

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Defining parameters

Level: \( N \) = \( 272 = 2^{4} \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 13 \)
Newform subspaces: \( 38 \)
Sturm bound: \(9216\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(272))\).

Total New Old
Modular forms 2528 1354 1174
Cusp forms 2081 1220 861
Eisenstein series 447 134 313

Trace form

\( 1220 q - 28 q^{2} - 20 q^{3} - 32 q^{4} - 36 q^{5} - 40 q^{6} - 24 q^{7} - 40 q^{8} - 8 q^{9} + O(q^{10}) \) \( 1220 q - 28 q^{2} - 20 q^{3} - 32 q^{4} - 36 q^{5} - 40 q^{6} - 24 q^{7} - 40 q^{8} - 8 q^{9} - 32 q^{10} - 28 q^{11} - 24 q^{12} - 36 q^{13} - 24 q^{14} - 32 q^{15} - 16 q^{16} - 68 q^{17} - 68 q^{18} - 36 q^{19} - 40 q^{20} - 48 q^{21} - 32 q^{22} - 24 q^{23} - 32 q^{24} - 8 q^{25} - 40 q^{26} - 8 q^{27} - 48 q^{28} - 52 q^{29} - 24 q^{30} + 8 q^{31} - 48 q^{32} - 72 q^{33} - 36 q^{34} - 40 q^{35} - 24 q^{36} - 52 q^{37} - 8 q^{38} - 24 q^{39} - 16 q^{40} - 8 q^{41} - 32 q^{42} - 44 q^{43} - 24 q^{44} - 44 q^{45} - 56 q^{46} - 56 q^{47} - 48 q^{48} - 84 q^{49} - 20 q^{50} - 28 q^{51} - 56 q^{52} - 36 q^{53} - 32 q^{54} - 72 q^{55} - 16 q^{56} - 72 q^{57} - 8 q^{58} - 60 q^{59} - 32 q^{60} - 68 q^{61} - 64 q^{62} - 176 q^{63} - 32 q^{64} - 144 q^{65} - 40 q^{66} - 44 q^{67} - 32 q^{68} - 184 q^{69} - 48 q^{70} - 72 q^{71} - 40 q^{72} - 72 q^{73} - 32 q^{74} - 180 q^{75} - 56 q^{76} - 112 q^{77} - 24 q^{78} - 72 q^{79} - 48 q^{80} - 156 q^{81} - 32 q^{82} - 68 q^{83} - 16 q^{84} - 60 q^{85} - 64 q^{86} - 24 q^{87} - 48 q^{88} - 8 q^{89} - 24 q^{90} - 32 q^{91} + 16 q^{92} - 72 q^{93} - 64 q^{97} - 20 q^{98} + 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(272))\)

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
272.2.a \(\chi_{272}(1, \cdot)\) 272.2.a.a 1 1
272.2.a.b 1
272.2.a.c 1
272.2.a.d 1
272.2.a.e 2
272.2.a.f 2
272.2.b \(\chi_{272}(33, \cdot)\) 272.2.b.a 2 1
272.2.b.b 2
272.2.b.c 2
272.2.b.d 2
272.2.c \(\chi_{272}(137, \cdot)\) None 0 1
272.2.h \(\chi_{272}(169, \cdot)\) None 0 1
272.2.j \(\chi_{272}(13, \cdot)\) 272.2.j.a 68 2
272.2.l \(\chi_{272}(69, \cdot)\) 272.2.l.a 2 2
272.2.l.b 30
272.2.l.c 32
272.2.m \(\chi_{272}(89, \cdot)\) None 0 2
272.2.o \(\chi_{272}(81, \cdot)\) 272.2.o.a 2 2
272.2.o.b 2
272.2.o.c 2
272.2.o.d 2
272.2.o.e 2
272.2.o.f 2
272.2.o.g 4
272.2.r \(\chi_{272}(101, \cdot)\) 272.2.r.a 68 2
272.2.s \(\chi_{272}(149, \cdot)\) 272.2.s.a 68 2
272.2.v \(\chi_{272}(49, \cdot)\) 272.2.v.a 4 4
272.2.v.b 4
272.2.v.c 4
272.2.v.d 4
272.2.v.e 4
272.2.v.f 12
272.2.w \(\chi_{272}(189, \cdot)\) 272.2.w.a 4 4
272.2.w.b 132
272.2.y \(\chi_{272}(53, \cdot)\) 272.2.y.a 4 4
272.2.y.b 132
272.2.ba \(\chi_{272}(9, \cdot)\) None 0 4
272.2.bd \(\chi_{272}(3, \cdot)\) 272.2.bd.a 272 8
272.2.bf \(\chi_{272}(31, \cdot)\) 272.2.bf.a 8 8
272.2.bf.b 16
272.2.bf.c 48
272.2.bg \(\chi_{272}(7, \cdot)\) None 0 8
272.2.bj \(\chi_{272}(107, \cdot)\) 272.2.bj.a 272 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(272))\) into lower level spaces

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