Properties

Label 1764.3
Level 1764
Weight 3
Dimension 74608
Nonzero newspaces 40
Sturm bound 508032
Trace bound 13

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Defining parameters

Level: \( N \) = \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(508032\)
Trace bound: \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1764))\).

Total New Old
Modular forms 171744 75482 96262
Cusp forms 166944 74608 92336
Eisenstein series 4800 874 3926

Trace form

\( 74608q - 44q^{2} + 3q^{3} - 42q^{4} - 85q^{5} - 69q^{6} + 4q^{7} - 89q^{8} - 135q^{9} + O(q^{10}) \) \( 74608q - 44q^{2} + 3q^{3} - 42q^{4} - 85q^{5} - 69q^{6} + 4q^{7} - 89q^{8} - 135q^{9} - 105q^{10} + 18q^{11} - 96q^{12} - 35q^{13} - 66q^{14} + 75q^{15} - 102q^{16} - 28q^{17} - 48q^{18} + 4q^{19} - 271q^{20} - 162q^{21} - 270q^{22} - 15q^{23} + 69q^{24} - 245q^{25} + 17q^{26} - 252q^{27} - 138q^{28} - 679q^{29} - 204q^{30} - 533q^{31} - 554q^{32} - 582q^{33} - 510q^{34} - 363q^{35} - 753q^{36} - 724q^{37} - 612q^{38} - 87q^{39} - 231q^{40} + 92q^{41} - 6q^{42} + 276q^{43} - 57q^{44} + 267q^{45} + 303q^{46} + 675q^{47} + 447q^{48} + 150q^{49} + 987q^{50} - 99q^{51} + 1011q^{52} + 74q^{53} + 825q^{54} + 363q^{55} + 564q^{56} - 441q^{57} + 897q^{58} - 234q^{59} + 816q^{60} - 162q^{61} + 1269q^{62} + 84q^{63} + 753q^{64} - 221q^{65} + 990q^{66} - 418q^{67} + 2132q^{68} - 243q^{69} + 1017q^{70} - 384q^{71} + 1203q^{72} - 2798q^{73} + 1541q^{74} + 687q^{75} + 918q^{76} - 603q^{77} + 42q^{78} - 1147q^{79} - 1258q^{80} - 975q^{81} - 2130q^{82} - 1257q^{83} - 180q^{84} - 840q^{85} - 2787q^{86} + 837q^{87} - 2919q^{88} + 2732q^{89} - 1476q^{90} + 520q^{91} - 2514q^{92} + 1599q^{93} - 3150q^{94} + 2442q^{95} - 1344q^{96} + 2614q^{97} - 1560q^{98} + 1419q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1764))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1764.3.c \(\chi_{1764}(197, \cdot)\) 1764.3.c.a 2 1
1764.3.c.b 2
1764.3.c.c 2
1764.3.c.d 2
1764.3.c.e 4
1764.3.c.f 4
1764.3.c.g 4
1764.3.c.h 8
1764.3.d \(\chi_{1764}(685, \cdot)\) 1764.3.d.a 2 1
1764.3.d.b 2
1764.3.d.c 2
1764.3.d.d 4
1764.3.d.e 4
1764.3.d.f 4
1764.3.d.g 8
1764.3.d.h 8
1764.3.g \(\chi_{1764}(883, \cdot)\) n/a 200 1
1764.3.h \(\chi_{1764}(1763, \cdot)\) n/a 160 1
1764.3.m \(\chi_{1764}(569, \cdot)\) n/a 160 2
1764.3.p \(\chi_{1764}(313, \cdot)\) n/a 160 2
1764.3.q \(\chi_{1764}(215, \cdot)\) n/a 320 2
1764.3.r \(\chi_{1764}(227, \cdot)\) n/a 944 2
1764.3.s \(\chi_{1764}(587, \cdot)\) n/a 944 2
1764.3.u \(\chi_{1764}(655, \cdot)\) n/a 944 2
1764.3.v \(\chi_{1764}(295, \cdot)\) n/a 964 2
1764.3.y \(\chi_{1764}(667, \cdot)\) n/a 392 2
1764.3.z \(\chi_{1764}(325, \cdot)\) 1764.3.z.a 2 2
1764.3.z.b 2
1764.3.z.c 2
1764.3.z.d 2
1764.3.z.e 2
1764.3.z.f 2
1764.3.z.g 2
1764.3.z.h 4
1764.3.z.i 4
1764.3.z.j 4
1764.3.z.k 8
1764.3.z.l 8
1764.3.z.m 8
1764.3.z.n 16
1764.3.bc \(\chi_{1764}(97, \cdot)\) n/a 160 2
1764.3.bd \(\chi_{1764}(1489, \cdot)\) n/a 160 2
1764.3.bg \(\chi_{1764}(785, \cdot)\) n/a 164 2
1764.3.bh \(\chi_{1764}(1145, \cdot)\) n/a 160 2
1764.3.bk \(\chi_{1764}(557, \cdot)\) 1764.3.bk.a 4 2
1764.3.bk.b 4
1764.3.bk.c 4
1764.3.bk.d 8
1764.3.bk.e 8
1764.3.bk.f 8
1764.3.bk.g 16
1764.3.bl \(\chi_{1764}(67, \cdot)\) n/a 944 2
1764.3.bn \(\chi_{1764}(803, \cdot)\) n/a 944 2
1764.3.bp \(\chi_{1764}(251, \cdot)\) n/a 1344 6
1764.3.bq \(\chi_{1764}(127, \cdot)\) n/a 1668 6
1764.3.bt \(\chi_{1764}(181, \cdot)\) n/a 276 6
1764.3.bu \(\chi_{1764}(449, \cdot)\) n/a 216 6
1764.3.ca \(\chi_{1764}(47, \cdot)\) n/a 8016 12
1764.3.cc \(\chi_{1764}(319, \cdot)\) n/a 8016 12
1764.3.cd \(\chi_{1764}(53, \cdot)\) n/a 456 12
1764.3.cg \(\chi_{1764}(137, \cdot)\) n/a 1344 12
1764.3.ch \(\chi_{1764}(29, \cdot)\) n/a 1344 12
1764.3.ck \(\chi_{1764}(229, \cdot)\) n/a 1344 12
1764.3.cl \(\chi_{1764}(13, \cdot)\) n/a 1344 12
1764.3.co \(\chi_{1764}(73, \cdot)\) n/a 564 12
1764.3.cp \(\chi_{1764}(163, \cdot)\) n/a 3336 12
1764.3.cs \(\chi_{1764}(43, \cdot)\) n/a 8016 12
1764.3.ct \(\chi_{1764}(151, \cdot)\) n/a 8016 12
1764.3.cv \(\chi_{1764}(83, \cdot)\) n/a 8016 12
1764.3.cw \(\chi_{1764}(131, \cdot)\) n/a 8016 12
1764.3.cx \(\chi_{1764}(143, \cdot)\) n/a 2688 12
1764.3.cy \(\chi_{1764}(61, \cdot)\) n/a 1344 12
1764.3.db \(\chi_{1764}(65, \cdot)\) n/a 1344 12

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1764))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(1764)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 18}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(441))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(588))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(882))\)\(^{\oplus 2}\)