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Properties

Label 1734.4
Level 1734
Weight 4
Dimension 61993
Nonzero newspaces 10
Sturm bound 665856
Trace bound 2

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Defining parameters

Level: \( N \) = \( 1734 = 2 \cdot 3 \cdot 17^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 10 \)
Sturm bound: \(665856\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1734))\).

Total New Old
Modular forms 251296 61993 189303
Cusp forms 248096 61993 186103
Eisenstein series 3200 0 3200

Trace form

\( 61993 q - 2 q^{2} - 3 q^{3} + 4 q^{4} + 6 q^{5} + 6 q^{6} - 16 q^{7} - 8 q^{8} + 9 q^{9} + O(q^{10}) \) \( 61993 q - 2 q^{2} - 3 q^{3} + 4 q^{4} + 6 q^{5} + 6 q^{6} - 16 q^{7} - 8 q^{8} + 9 q^{9} + 404 q^{10} + 908 q^{11} + 52 q^{12} - 218 q^{13} - 608 q^{14} - 1362 q^{15} - 240 q^{16} - 512 q^{17} - 914 q^{18} - 620 q^{19} - 40 q^{20} + 432 q^{21} + 872 q^{22} + 1832 q^{23} + 664 q^{24} + 6615 q^{25} + 1108 q^{26} - 27 q^{27} - 64 q^{28} - 1010 q^{29} + 36 q^{30} - 3544 q^{31} - 32 q^{32} - 2148 q^{33} - 4064 q^{35} + 36 q^{36} - 2434 q^{37} - 40 q^{38} - 5554 q^{39} - 48 q^{40} + 1882 q^{41} - 2208 q^{42} + 5420 q^{43} + 48 q^{44} + 4198 q^{45} - 336 q^{46} - 96 q^{47} - 48 q^{48} - 87 q^{49} + 178 q^{50} + 3200 q^{51} + 152 q^{52} + 2486 q^{53} + 4310 q^{54} + 5768 q^{55} + 128 q^{56} + 1908 q^{57} - 60 q^{58} - 340 q^{59} - 2632 q^{60} - 2138 q^{61} + 176 q^{62} - 14832 q^{63} + 64 q^{64} - 748 q^{65} - 2968 q^{66} - 3404 q^{67} + 1504 q^{68} + 5320 q^{69} + 16320 q^{70} + 9816 q^{71} + 1080 q^{72} + 14986 q^{73} + 3236 q^{74} - 21 q^{75} + 80 q^{76} - 5888 q^{77} - 5148 q^{78} - 10184 q^{79} - 4000 q^{80} + 1921 q^{81} - 21300 q^{82} - 5164 q^{83} - 5184 q^{84} - 14216 q^{85} - 10392 q^{86} - 25530 q^{87} - 9312 q^{88} - 11478 q^{89} - 972 q^{90} - 16736 q^{91} - 1120 q^{92} + 2440 q^{93} + 1728 q^{94} + 6776 q^{95} + 96 q^{96} + 19586 q^{97} + 14286 q^{98} + 38620 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1734))\)

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
1734.4.a \(\chi_{1734}(1, \cdot)\) 1734.4.a.a 1 1
1734.4.a.b 1
1734.4.a.c 1
1734.4.a.d 1
1734.4.a.e 1
1734.4.a.f 1
1734.4.a.g 1
1734.4.a.h 2
1734.4.a.i 2
1734.4.a.j 2
1734.4.a.k 2
1734.4.a.l 2
1734.4.a.m 2
1734.4.a.n 2
1734.4.a.o 2
1734.4.a.p 2
1734.4.a.q 2
1734.4.a.r 2
1734.4.a.s 2
1734.4.a.t 3
1734.4.a.u 3
1734.4.a.v 3
1734.4.a.w 3
1734.4.a.x 3
1734.4.a.y 3
1734.4.a.z 6
1734.4.a.ba 6
1734.4.a.bb 6
1734.4.a.bc 6
1734.4.a.bd 6
1734.4.a.be 6
1734.4.a.bf 8
1734.4.a.bg 8
1734.4.a.bh 8
1734.4.a.bi 8
1734.4.a.bj 9
1734.4.a.bk 9
1734.4.b \(\chi_{1734}(577, \cdot)\) n/a 134 1
1734.4.f \(\chi_{1734}(829, \cdot)\) n/a 268 2
1734.4.h \(\chi_{1734}(733, \cdot)\) n/a 544 4
1734.4.i \(\chi_{1734}(65, \cdot)\) n/a 2160 8
1734.4.k \(\chi_{1734}(103, \cdot)\) n/a 2464 16
1734.4.n \(\chi_{1734}(67, \cdot)\) n/a 2464 16
1734.4.o \(\chi_{1734}(13, \cdot)\) n/a 4928 32
1734.4.q \(\chi_{1734}(19, \cdot)\) n/a 9728 64
1734.4.t \(\chi_{1734}(5, \cdot)\) n/a 39168 128

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1734))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1734)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(578))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(867))\)\(^{\oplus 2}\)