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Properties

Label 544.2
Level 544
Weight 2
Dimension 4998
Nonzero newspaces 22
Newform subspaces 62
Sturm bound 36864
Trace bound 10

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Defining parameters

Level: \( N \) = \( 544 = 2^{5} \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 22 \)
Newform subspaces: \( 62 \)
Sturm bound: \(36864\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(544))\).

Total New Old
Modular forms 9728 5298 4430
Cusp forms 8705 4998 3707
Eisenstein series 1023 300 723

Trace form

\( 4998 q - 56 q^{2} - 40 q^{3} - 56 q^{4} - 52 q^{5} - 56 q^{6} - 40 q^{7} - 56 q^{8} - 82 q^{9} + O(q^{10}) \) \( 4998 q - 56 q^{2} - 40 q^{3} - 56 q^{4} - 52 q^{5} - 56 q^{6} - 40 q^{7} - 56 q^{8} - 82 q^{9} - 72 q^{10} - 40 q^{11} - 88 q^{12} - 68 q^{13} - 88 q^{14} - 48 q^{15} - 96 q^{16} - 34 q^{17} - 160 q^{18} - 40 q^{19} - 88 q^{20} - 56 q^{21} - 80 q^{22} - 56 q^{23} - 32 q^{24} - 86 q^{25} - 16 q^{26} - 88 q^{27} - 16 q^{28} - 36 q^{29} + 8 q^{30} - 80 q^{31} - 16 q^{32} - 144 q^{33} - 48 q^{34} - 136 q^{35} - 52 q^{37} - 72 q^{38} - 88 q^{39} - 80 q^{40} - 108 q^{41} - 96 q^{42} - 56 q^{43} - 136 q^{44} - 92 q^{45} - 120 q^{46} - 48 q^{47} - 160 q^{48} - 18 q^{49} - 136 q^{50} - 40 q^{51} - 136 q^{52} - 116 q^{53} - 80 q^{54} + 24 q^{55} - 80 q^{56} - 88 q^{57} - 48 q^{58} + 24 q^{59} - 48 q^{60} - 100 q^{61} - 16 q^{62} + 48 q^{63} + 16 q^{64} - 120 q^{65} - 8 q^{66} + 24 q^{67} - 80 q^{68} - 184 q^{69} - 32 q^{70} + 24 q^{71} - 104 q^{72} - 76 q^{73} - 88 q^{74} - 16 q^{75} - 56 q^{76} - 88 q^{77} - 136 q^{78} - 48 q^{79} - 48 q^{80} - 50 q^{81} - 56 q^{82} - 120 q^{83} - 96 q^{84} - 76 q^{85} - 80 q^{86} - 152 q^{87} - 64 q^{88} - 108 q^{89} - 80 q^{90} - 136 q^{91} + 16 q^{92} - 32 q^{93} - 80 q^{94} - 160 q^{95} - 64 q^{96} - 180 q^{97} - 16 q^{98} - 192 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(544))\)

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
544.2.a \(\chi_{544}(1, \cdot)\) 544.2.a.a 1 1
544.2.a.b 1
544.2.a.c 1
544.2.a.d 1
544.2.a.e 1
544.2.a.f 1
544.2.a.g 2
544.2.a.h 2
544.2.a.i 3
544.2.a.j 3
544.2.b \(\chi_{544}(33, \cdot)\) 544.2.b.a 2 1
544.2.b.b 4
544.2.b.c 4
544.2.b.d 4
544.2.b.e 4
544.2.c \(\chi_{544}(273, \cdot)\) 544.2.c.a 8 1
544.2.c.b 8
544.2.h \(\chi_{544}(305, \cdot)\) 544.2.h.a 16 1
544.2.j \(\chi_{544}(89, \cdot)\) None 0 2
544.2.l \(\chi_{544}(137, \cdot)\) None 0 2
544.2.m \(\chi_{544}(81, \cdot)\) 544.2.m.a 8 2
544.2.m.b 24
544.2.o \(\chi_{544}(225, \cdot)\) 544.2.o.a 2 2
544.2.o.b 2
544.2.o.c 2
544.2.o.d 2
544.2.o.e 2
544.2.o.f 2
544.2.o.g 6
544.2.o.h 6
544.2.o.i 12
544.2.r \(\chi_{544}(169, \cdot)\) None 0 2
544.2.s \(\chi_{544}(217, \cdot)\) None 0 2
544.2.v \(\chi_{544}(253, \cdot)\) 544.2.v.a 280 4
544.2.x \(\chi_{544}(77, \cdot)\) 544.2.x.a 280 4
544.2.z \(\chi_{544}(13, \cdot)\) 544.2.z.a 280 4
544.2.bb \(\chi_{544}(161, \cdot)\) 544.2.bb.a 4 4
544.2.bb.b 4
544.2.bb.c 8
544.2.bb.d 16
544.2.bb.e 20
544.2.bb.f 20
544.2.bc \(\chi_{544}(101, \cdot)\) 544.2.bc.a 280 4
544.2.bd \(\chi_{544}(69, \cdot)\) 544.2.bd.a 128 4
544.2.bd.b 128
544.2.be \(\chi_{544}(25, \cdot)\) None 0 4
544.2.bg \(\chi_{544}(9, \cdot)\) None 0 4
544.2.bk \(\chi_{544}(49, \cdot)\) 544.2.bk.a 64 4
544.2.bn \(\chi_{544}(149, \cdot)\) 544.2.bn.a 280 4
544.2.bp \(\chi_{544}(53, \cdot)\) 544.2.bp.a 280 4
544.2.bq \(\chi_{544}(189, \cdot)\) 544.2.bq.a 280 4
544.2.bt \(\chi_{544}(7, \cdot)\) None 0 8
544.2.bu \(\chi_{544}(75, \cdot)\) 544.2.bu.a 560 8
544.2.bx \(\chi_{544}(31, \cdot)\) 544.2.bx.a 8 8
544.2.bx.b 8
544.2.bx.c 8
544.2.bx.d 8
544.2.bx.e 8
544.2.bx.f 8
544.2.bx.g 8
544.2.bx.h 8
544.2.bx.i 40
544.2.bx.j 40
544.2.bz \(\chi_{544}(107, \cdot)\) 544.2.bz.a 560 8
544.2.cb \(\chi_{544}(139, \cdot)\) 544.2.cb.a 560 8
544.2.cc \(\chi_{544}(79, \cdot)\) 544.2.cc.a 8 8
544.2.cc.b 8
544.2.cc.c 112
544.2.ce \(\chi_{544}(3, \cdot)\) 544.2.ce.a 560 8
544.2.ch \(\chi_{544}(23, \cdot)\) None 0 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(544))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(544)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(272))\)\(^{\oplus 2}\)