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Properties

Label 1722.2
Level 1722
Weight 2
Dimension 19293
Nonzero newspaces 32
Sturm bound 322560
Trace bound 15

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Defining parameters

Level: \( N \) = \( 1722 = 2 \cdot 3 \cdot 7 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(322560\)
Trace bound: \(15\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1722))\).

Total New Old
Modular forms 82560 19293 63267
Cusp forms 78721 19293 59428
Eisenstein series 3839 0 3839

Trace form

\( 19293 q - 3 q^{2} + q^{3} + 5 q^{4} + 6 q^{5} + 9 q^{6} + 17 q^{7} - 3 q^{8} + 13 q^{9} + O(q^{10}) \) \( 19293 q - 3 q^{2} + q^{3} + 5 q^{4} + 6 q^{5} + 9 q^{6} + 17 q^{7} - 3 q^{8} + 13 q^{9} + 6 q^{10} + 12 q^{11} + q^{12} - 10 q^{13} - 15 q^{14} - 18 q^{15} - 3 q^{16} - 30 q^{17} - 27 q^{18} - 28 q^{19} - 18 q^{20} - 35 q^{21} - 36 q^{22} - 48 q^{23} - 15 q^{24} - 45 q^{25} - 18 q^{26} + q^{27} + 9 q^{28} - 42 q^{29} + 86 q^{30} + 144 q^{31} + 37 q^{32} + 252 q^{33} + 194 q^{34} + 166 q^{35} + 53 q^{36} + 478 q^{37} + 172 q^{38} + 334 q^{39} + 166 q^{40} + 125 q^{41} + 205 q^{42} + 188 q^{43} + 172 q^{44} + 326 q^{45} + 184 q^{46} + 408 q^{47} + 41 q^{48} + 157 q^{49} + 203 q^{50} + 162 q^{51} - 18 q^{52} + 70 q^{53} + 41 q^{54} - 144 q^{55} + 9 q^{56} - 4 q^{57} - 114 q^{58} - 84 q^{59} - 42 q^{60} - 106 q^{61} - 48 q^{62} - 47 q^{63} + 5 q^{64} - 44 q^{65} - 36 q^{66} + 84 q^{67} - 30 q^{68} + 136 q^{69} - 90 q^{70} + 248 q^{71} + 21 q^{72} + 202 q^{73} - 42 q^{74} + 303 q^{75} - 28 q^{76} + 196 q^{77} + 6 q^{78} + 320 q^{79} + 6 q^{80} + 149 q^{81} - 11 q^{82} + 308 q^{83} + 37 q^{84} + 740 q^{85} - 12 q^{86} + 190 q^{87} - 12 q^{88} + 242 q^{89} + 6 q^{90} + 334 q^{91} - 24 q^{92} + 120 q^{93} + 176 q^{95} - 15 q^{96} + 226 q^{97} - 51 q^{98} - 36 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1722))\)

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
1722.2.a \(\chi_{1722}(1, \cdot)\) 1722.2.a.a 1 1
1722.2.a.b 1
1722.2.a.c 1
1722.2.a.d 1
1722.2.a.e 1
1722.2.a.f 1
1722.2.a.g 1
1722.2.a.h 1
1722.2.a.i 1
1722.2.a.j 1
1722.2.a.k 1
1722.2.a.l 1
1722.2.a.m 1
1722.2.a.n 1
1722.2.a.o 1
1722.2.a.p 1
1722.2.a.q 1
1722.2.a.r 2
1722.2.a.s 2
1722.2.a.t 2
1722.2.a.u 2
1722.2.a.v 2
1722.2.a.w 3
1722.2.a.x 3
1722.2.a.y 3
1722.2.a.z 5
1722.2.f \(\chi_{1722}(1639, \cdot)\) 1722.2.f.a 2 1
1722.2.f.b 2
1722.2.f.c 2
1722.2.f.d 2
1722.2.f.e 2
1722.2.f.f 2
1722.2.f.g 4
1722.2.f.h 8
1722.2.f.i 10
1722.2.f.j 10
1722.2.g \(\chi_{1722}(83, \cdot)\) n/a 104 1
1722.2.h \(\chi_{1722}(1721, \cdot)\) n/a 112 1
1722.2.i \(\chi_{1722}(247, \cdot)\) n/a 104 2
1722.2.j \(\chi_{1722}(419, \cdot)\) n/a 224 2
1722.2.k \(\chi_{1722}(337, \cdot)\) 1722.2.k.a 4 2
1722.2.k.b 4
1722.2.k.c 8
1722.2.k.d 8
1722.2.k.e 16
1722.2.k.f 16
1722.2.k.g 24
1722.2.n \(\chi_{1722}(379, \cdot)\) n/a 176 4
1722.2.o \(\chi_{1722}(983, \cdot)\) n/a 224 2
1722.2.p \(\chi_{1722}(1067, \cdot)\) n/a 216 2
1722.2.q \(\chi_{1722}(163, \cdot)\) n/a 112 2
1722.2.w \(\chi_{1722}(55, \cdot)\) n/a 224 4
1722.2.x \(\chi_{1722}(407, \cdot)\) n/a 336 4
1722.2.z \(\chi_{1722}(209, \cdot)\) n/a 448 4
1722.2.ba \(\chi_{1722}(461, \cdot)\) n/a 448 4
1722.2.bb \(\chi_{1722}(127, \cdot)\) n/a 176 4
1722.2.bi \(\chi_{1722}(319, \cdot)\) n/a 224 4
1722.2.bj \(\chi_{1722}(173, \cdot)\) n/a 448 4
1722.2.bk \(\chi_{1722}(37, \cdot)\) n/a 448 8
1722.2.bn \(\chi_{1722}(43, \cdot)\) n/a 320 8
1722.2.bo \(\chi_{1722}(125, \cdot)\) n/a 896 8
1722.2.bq \(\chi_{1722}(137, \cdot)\) n/a 896 8
1722.2.br \(\chi_{1722}(325, \cdot)\) n/a 448 8
1722.2.bx \(\chi_{1722}(25, \cdot)\) n/a 448 8
1722.2.by \(\chi_{1722}(59, \cdot)\) n/a 896 8
1722.2.bz \(\chi_{1722}(269, \cdot)\) n/a 896 8
1722.2.cb \(\chi_{1722}(29, \cdot)\) n/a 1344 16
1722.2.cc \(\chi_{1722}(13, \cdot)\) n/a 896 16
1722.2.ce \(\chi_{1722}(5, \cdot)\) n/a 1792 16
1722.2.cf \(\chi_{1722}(121, \cdot)\) n/a 896 16
1722.2.cj \(\chi_{1722}(19, \cdot)\) n/a 1792 32
1722.2.ck \(\chi_{1722}(11, \cdot)\) n/a 3584 32

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1722))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1722)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(123))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(246))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(287))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(574))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(861))\)\(^{\oplus 2}\)