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Properties

Label 3483.2
Level 3483
Weight 2
Dimension 352136
Nonzero newspaces 44
Sturm bound 1796256
Trace bound 26

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Defining parameters

Level: \( N \) = \( 3483 = 3^{4} \cdot 43 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 44 \)
Sturm bound: \(1796256\)
Trace bound: \(26\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3483))\).

Total New Old
Modular forms 453600 356728 96872
Cusp forms 444529 352136 92393
Eisenstein series 9071 4592 4479

Trace form

\( 352136 q - 480 q^{2} - 720 q^{3} - 796 q^{4} - 474 q^{5} - 720 q^{6} - 794 q^{7} - 456 q^{8} - 720 q^{9} + O(q^{10}) \) \( 352136 q - 480 q^{2} - 720 q^{3} - 796 q^{4} - 474 q^{5} - 720 q^{6} - 794 q^{7} - 456 q^{8} - 720 q^{9} - 1140 q^{10} - 462 q^{11} - 720 q^{12} - 782 q^{13} - 438 q^{14} - 720 q^{15} - 796 q^{16} - 450 q^{17} - 738 q^{18} - 1172 q^{19} - 546 q^{20} - 774 q^{21} - 810 q^{22} - 546 q^{23} - 828 q^{24} - 820 q^{25} - 654 q^{26} - 774 q^{27} - 1208 q^{28} - 534 q^{29} - 828 q^{30} - 818 q^{31} - 576 q^{32} - 774 q^{33} - 822 q^{34} - 498 q^{35} - 792 q^{36} - 1136 q^{37} - 402 q^{38} - 720 q^{39} - 846 q^{40} - 474 q^{41} - 810 q^{42} - 817 q^{43} - 1110 q^{44} - 828 q^{45} - 1248 q^{46} - 606 q^{47} - 918 q^{48} - 840 q^{49} - 768 q^{50} - 846 q^{51} - 878 q^{52} - 630 q^{53} - 972 q^{54} - 1248 q^{55} - 822 q^{56} - 828 q^{57} - 846 q^{58} - 618 q^{59} - 954 q^{60} - 830 q^{61} - 690 q^{62} - 828 q^{63} - 1186 q^{64} - 498 q^{65} - 720 q^{66} - 818 q^{67} - 288 q^{68} - 612 q^{69} - 882 q^{70} - 270 q^{71} - 288 q^{72} - 1082 q^{73} - 114 q^{74} - 540 q^{75} - 842 q^{76} - 150 q^{77} - 486 q^{78} - 794 q^{79} + 156 q^{80} - 576 q^{81} - 2112 q^{82} - 246 q^{83} - 270 q^{84} - 858 q^{85} - 291 q^{86} - 1188 q^{87} - 906 q^{88} - 324 q^{89} - 558 q^{90} - 1150 q^{91} - 294 q^{92} - 756 q^{93} - 882 q^{94} - 606 q^{95} - 702 q^{96} - 902 q^{97} - 756 q^{98} - 864 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3483))\)

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
3483.2.a \(\chi_{3483}(1, \cdot)\) 3483.2.a.a 1 1
3483.2.a.b 1
3483.2.a.c 1
3483.2.a.d 1
3483.2.a.e 1
3483.2.a.f 1
3483.2.a.g 2
3483.2.a.h 2
3483.2.a.i 3
3483.2.a.j 3
3483.2.a.k 4
3483.2.a.l 4
3483.2.a.m 6
3483.2.a.n 6
3483.2.a.o 7
3483.2.a.p 7
3483.2.a.q 16
3483.2.a.r 19
3483.2.a.s 19
3483.2.a.t 20
3483.2.a.u 20
3483.2.a.v 24
3483.2.d \(\chi_{3483}(3482, \cdot)\) n/a 172 1
3483.2.e \(\chi_{3483}(1081, \cdot)\) n/a 348 2
3483.2.f \(\chi_{3483}(1162, \cdot)\) n/a 336 2
3483.2.g \(\chi_{3483}(595, \cdot)\) n/a 348 2
3483.2.h \(\chi_{3483}(2917, \cdot)\) n/a 344 2
3483.2.k \(\chi_{3483}(1727, \cdot)\) n/a 348 2
3483.2.l \(\chi_{3483}(1160, \cdot)\) n/a 348 2
3483.2.m \(\chi_{3483}(1241, \cdot)\) n/a 348 2
3483.2.t \(\chi_{3483}(80, \cdot)\) n/a 344 2
3483.2.u \(\chi_{3483}(649, \cdot)\) n/a 1032 6
3483.2.v \(\chi_{3483}(388, \cdot)\) n/a 756 6
3483.2.w \(\chi_{3483}(208, \cdot)\) n/a 780 6
3483.2.x \(\chi_{3483}(694, \cdot)\) n/a 780 6
3483.2.y \(\chi_{3483}(161, \cdot)\) n/a 1032 6
3483.2.bb \(\chi_{3483}(854, \cdot)\) n/a 780 6
3483.2.bc \(\chi_{3483}(386, \cdot)\) n/a 780 6
3483.2.bd \(\chi_{3483}(179, \cdot)\) n/a 780 6
3483.2.bk \(\chi_{3483}(325, \cdot)\) n/a 2064 12
3483.2.bl \(\chi_{3483}(271, \cdot)\) n/a 2088 12
3483.2.bm \(\chi_{3483}(379, \cdot)\) n/a 2088 12
3483.2.bn \(\chi_{3483}(109, \cdot)\) n/a 2088 12
3483.2.bo \(\chi_{3483}(130, \cdot)\) n/a 6804 18
3483.2.bp \(\chi_{3483}(49, \cdot)\) n/a 7092 18
3483.2.bq \(\chi_{3483}(178, \cdot)\) n/a 7092 18
3483.2.br \(\chi_{3483}(485, \cdot)\) n/a 2064 12
3483.2.by \(\chi_{3483}(458, \cdot)\) n/a 2088 12
3483.2.bz \(\chi_{3483}(512, \cdot)\) n/a 2088 12
3483.2.ca \(\chi_{3483}(26, \cdot)\) n/a 2088 12
3483.2.cf \(\chi_{3483}(308, \cdot)\) n/a 7092 18
3483.2.cg \(\chi_{3483}(128, \cdot)\) n/a 7092 18
3483.2.cl \(\chi_{3483}(50, \cdot)\) n/a 7092 18
3483.2.cm \(\chi_{3483}(289, \cdot)\) n/a 4680 36
3483.2.cn \(\chi_{3483}(10, \cdot)\) n/a 4680 36
3483.2.co \(\chi_{3483}(64, \cdot)\) n/a 4680 36
3483.2.cv \(\chi_{3483}(62, \cdot)\) n/a 4680 36
3483.2.cw \(\chi_{3483}(8, \cdot)\) n/a 4680 36
3483.2.cx \(\chi_{3483}(98, \cdot)\) n/a 4680 36
3483.2.cy \(\chi_{3483}(13, \cdot)\) n/a 42552 108
3483.2.cz \(\chi_{3483}(25, \cdot)\) n/a 42552 108
3483.2.da \(\chi_{3483}(4, \cdot)\) n/a 42552 108
3483.2.db \(\chi_{3483}(20, \cdot)\) n/a 42552 108
3483.2.dg \(\chi_{3483}(2, \cdot)\) n/a 42552 108
3483.2.dh \(\chi_{3483}(5, \cdot)\) n/a 42552 108

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3483))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3483)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(129))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(387))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1161))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3483))\)\(^{\oplus 1}\)