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Properties

Label 744.2
Level 744
Weight 2
Dimension 6350
Nonzero newspaces 24
Newform subspaces 59
Sturm bound 61440
Trace bound 6

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Defining parameters

Level: \( N \) = \( 744 = 2^{3} \cdot 3 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Newform subspaces: \( 59 \)
Sturm bound: \(61440\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(744))\).

Total New Old
Modular forms 16080 6582 9498
Cusp forms 14641 6350 8291
Eisenstein series 1439 232 1207

Trace form

\( 6350 q + 4 q^{2} - 24 q^{3} - 52 q^{4} + 4 q^{5} - 34 q^{6} - 52 q^{7} - 8 q^{8} - 54 q^{9} + O(q^{10}) \) \( 6350 q + 4 q^{2} - 24 q^{3} - 52 q^{4} + 4 q^{5} - 34 q^{6} - 52 q^{7} - 8 q^{8} - 54 q^{9} - 68 q^{10} - 8 q^{11} - 46 q^{12} + 4 q^{13} - 8 q^{14} - 42 q^{15} - 60 q^{16} + 4 q^{17} - 18 q^{18} - 60 q^{19} + 16 q^{20} - 44 q^{22} - 6 q^{24} - 102 q^{25} + 16 q^{26} - 48 q^{27} - 60 q^{28} - 12 q^{29} - 22 q^{30} - 72 q^{31} - 16 q^{32} - 68 q^{33} - 100 q^{34} - 38 q^{36} - 12 q^{37} - 16 q^{38} - 18 q^{39} - 76 q^{40} + 4 q^{41} - 38 q^{42} - 28 q^{43} + 4 q^{45} - 44 q^{46} + 48 q^{47} - 14 q^{48} - 62 q^{49} + 4 q^{50} + 96 q^{51} - 92 q^{52} + 64 q^{53} - 42 q^{54} + 76 q^{55} + 16 q^{56} + 14 q^{57} - 36 q^{58} + 52 q^{59} - 30 q^{60} + 184 q^{61} + 4 q^{62} + 52 q^{63} - 28 q^{64} + 140 q^{65} - 46 q^{66} - 48 q^{67} + 74 q^{69} - 44 q^{70} + 56 q^{71} - 54 q^{72} - 64 q^{73} - 32 q^{74} + 38 q^{75} - 12 q^{76} + 60 q^{77} - 46 q^{78} - 84 q^{79} - 38 q^{81} + 12 q^{82} + 8 q^{83} - 14 q^{84} + 8 q^{85} + 16 q^{86} + 6 q^{87} - 92 q^{88} + 52 q^{89} - 22 q^{90} - 60 q^{91} + 8 q^{93} - 168 q^{94} + 16 q^{95} - 78 q^{96} - 76 q^{97} - 12 q^{98} - 6 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(744))\)

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
744.2.a \(\chi_{744}(1, \cdot)\) 744.2.a.a 1 1
744.2.a.b 1
744.2.a.c 1
744.2.a.d 1
744.2.a.e 1
744.2.a.f 1
744.2.a.g 1
744.2.a.h 2
744.2.a.i 2
744.2.a.j 3
744.2.c \(\chi_{744}(619, \cdot)\) 744.2.c.a 64 1
744.2.e \(\chi_{744}(311, \cdot)\) None 0 1
744.2.f \(\chi_{744}(373, \cdot)\) 744.2.f.a 2 1
744.2.f.b 2
744.2.f.c 20
744.2.f.d 36
744.2.h \(\chi_{744}(185, \cdot)\) 744.2.h.a 32 1
744.2.j \(\chi_{744}(683, \cdot)\) 744.2.j.a 120 1
744.2.l \(\chi_{744}(247, \cdot)\) None 0 1
744.2.o \(\chi_{744}(557, \cdot)\) 744.2.o.a 4 1
744.2.o.b 4
744.2.o.c 4
744.2.o.d 16
744.2.o.e 96
744.2.q \(\chi_{744}(25, \cdot)\) 744.2.q.a 2 2
744.2.q.b 2
744.2.q.c 2
744.2.q.d 4
744.2.q.e 6
744.2.q.f 6
744.2.q.g 10
744.2.r \(\chi_{744}(97, \cdot)\) 744.2.r.a 4 4
744.2.r.b 4
744.2.r.c 12
744.2.r.d 12
744.2.r.e 16
744.2.r.f 16
744.2.t \(\chi_{744}(533, \cdot)\) 744.2.t.a 4 2
744.2.t.b 4
744.2.t.c 240
744.2.w \(\chi_{744}(223, \cdot)\) None 0 2
744.2.y \(\chi_{744}(563, \cdot)\) 744.2.y.a 248 2
744.2.ba \(\chi_{744}(161, \cdot)\) 744.2.ba.a 64 2
744.2.bc \(\chi_{744}(253, \cdot)\) 744.2.bc.a 128 2
744.2.bd \(\chi_{744}(191, \cdot)\) None 0 2
744.2.bf \(\chi_{744}(595, \cdot)\) 744.2.bf.a 128 2
744.2.bi \(\chi_{744}(89, \cdot)\) 744.2.bi.a 128 4
744.2.bk \(\chi_{744}(109, \cdot)\) 744.2.bk.a 256 4
744.2.bl \(\chi_{744}(47, \cdot)\) None 0 4
744.2.bn \(\chi_{744}(91, \cdot)\) 744.2.bn.a 256 4
744.2.bq \(\chi_{744}(29, \cdot)\) 744.2.bq.a 16 4
744.2.bq.b 480
744.2.bt \(\chi_{744}(151, \cdot)\) None 0 4
744.2.bv \(\chi_{744}(35, \cdot)\) 744.2.bv.a 496 4
744.2.bw \(\chi_{744}(49, \cdot)\) 744.2.bw.a 24 8
744.2.bw.b 32
744.2.bw.c 32
744.2.bw.d 40
744.2.bx \(\chi_{744}(59, \cdot)\) 744.2.bx.a 992 8
744.2.bz \(\chi_{744}(55, \cdot)\) None 0 8
744.2.cc \(\chi_{744}(53, \cdot)\) 744.2.cc.a 16 8
744.2.cc.b 16
744.2.cc.c 960
744.2.cf \(\chi_{744}(43, \cdot)\) 744.2.cf.a 512 8
744.2.ch \(\chi_{744}(71, \cdot)\) None 0 8
744.2.ci \(\chi_{744}(133, \cdot)\) 744.2.ci.a 512 8
744.2.ck \(\chi_{744}(17, \cdot)\) 744.2.ck.a 256 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(744))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(744)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(124))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(186))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(248))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(372))\)\(^{\oplus 2}\)