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Properties

Label 3005.2
Level 3005
Weight 2
Dimension 329299
Nonzero newspaces 48
Sturm bound 1444800
Trace bound 10

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Defining parameters

Level: \( N \) = \( 3005 = 5 \cdot 601 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(1444800\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3005))\).

Total New Old
Modular forms 363600 332895 30705
Cusp forms 358801 329299 29502
Eisenstein series 4799 3596 1203

Trace form

\( 329299 q - 603 q^{2} - 604 q^{3} - 607 q^{4} - 901 q^{5} - 1812 q^{6} - 608 q^{7} - 615 q^{8} - 613 q^{9} + O(q^{10}) \) \( 329299 q - 603 q^{2} - 604 q^{3} - 607 q^{4} - 901 q^{5} - 1812 q^{6} - 608 q^{7} - 615 q^{8} - 613 q^{9} - 903 q^{10} - 1812 q^{11} - 628 q^{12} - 614 q^{13} - 624 q^{14} - 904 q^{15} - 1831 q^{16} - 618 q^{17} - 639 q^{18} - 620 q^{19} - 907 q^{20} - 1832 q^{21} - 636 q^{22} - 624 q^{23} - 660 q^{24} - 901 q^{25} - 1842 q^{26} - 640 q^{27} - 656 q^{28} - 630 q^{29} - 912 q^{30} - 1832 q^{31} - 663 q^{32} - 648 q^{33} - 654 q^{34} - 908 q^{35} - 1891 q^{36} - 638 q^{37} - 660 q^{38} - 656 q^{39} - 915 q^{40} - 1842 q^{41} - 696 q^{42} - 644 q^{43} - 684 q^{44} - 913 q^{45} - 1872 q^{46} - 648 q^{47} - 724 q^{48} - 657 q^{49} - 903 q^{50} - 1872 q^{51} - 698 q^{52} - 654 q^{53} - 720 q^{54} - 912 q^{55} - 1920 q^{56} - 680 q^{57} - 690 q^{58} - 660 q^{59} - 928 q^{60} - 1862 q^{61} - 696 q^{62} - 704 q^{63} - 727 q^{64} - 914 q^{65} - 1944 q^{66} - 668 q^{67} - 726 q^{68} - 696 q^{69} - 924 q^{70} - 1872 q^{71} - 795 q^{72} - 674 q^{73} - 714 q^{74} - 904 q^{75} - 1940 q^{76} - 696 q^{77} - 768 q^{78} - 680 q^{79} - 931 q^{80} - 1921 q^{81} - 726 q^{82} - 684 q^{83} - 824 q^{84} - 918 q^{85} - 1932 q^{86} - 720 q^{87} - 780 q^{88} - 690 q^{89} - 939 q^{90} - 1912 q^{91} - 768 q^{92} - 728 q^{93} - 744 q^{94} - 920 q^{95} - 2052 q^{96} - 698 q^{97} - 771 q^{98} - 756 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3005))\)

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
3005.2.a \(\chi_{3005}(1, \cdot)\) 3005.2.a.a 43 1
3005.2.a.b 44
3005.2.a.c 57
3005.2.a.d 57
3005.2.b \(\chi_{3005}(1804, \cdot)\) n/a 300 1
3005.2.c \(\chi_{3005}(3004, \cdot)\) n/a 300 1
3005.2.d \(\chi_{3005}(1201, \cdot)\) n/a 202 1
3005.2.e \(\chi_{3005}(576, \cdot)\) n/a 400 2
3005.2.f \(\chi_{3005}(2279, \cdot)\) n/a 596 2
3005.2.k \(\chi_{3005}(476, \cdot)\) n/a 404 2
3005.2.l \(\chi_{3005}(1516, \cdot)\) n/a 808 4
3005.2.m \(\chi_{3005}(1779, \cdot)\) n/a 600 2
3005.2.n \(\chi_{3005}(24, \cdot)\) n/a 600 2
3005.2.o \(\chi_{3005}(626, \cdot)\) n/a 400 2
3005.2.q \(\chi_{3005}(163, \cdot)\) n/a 1196 4
3005.2.r \(\chi_{3005}(1143, \cdot)\) n/a 1196 4
3005.2.t \(\chi_{3005}(1371, \cdot)\) n/a 808 4
3005.2.u \(\chi_{3005}(169, \cdot)\) n/a 1200 4
3005.2.v \(\chi_{3005}(314, \cdot)\) n/a 1200 4
3005.2.w \(\chi_{3005}(2284, \cdot)\) n/a 1192 4
3005.2.bb \(\chi_{3005}(481, \cdot)\) n/a 800 4
3005.2.bc \(\chi_{3005}(151, \cdot)\) n/a 1600 8
3005.2.bd \(\chi_{3005}(416, \cdot)\) n/a 1616 8
3005.2.bi \(\chi_{3005}(394, \cdot)\) n/a 2384 8
3005.2.bk \(\chi_{3005}(387, \cdot)\) n/a 2392 8
3005.2.bl \(\chi_{3005}(132, \cdot)\) n/a 2392 8
3005.2.bn \(\chi_{3005}(16, \cdot)\) n/a 4040 20
3005.2.bo \(\chi_{3005}(666, \cdot)\) n/a 1600 8
3005.2.bp \(\chi_{3005}(324, \cdot)\) n/a 2400 8
3005.2.bq \(\chi_{3005}(199, \cdot)\) n/a 2400 8
3005.2.bs \(\chi_{3005}(193, \cdot)\) n/a 4784 16
3005.2.bt \(\chi_{3005}(97, \cdot)\) n/a 4784 16
3005.2.bv \(\chi_{3005}(111, \cdot)\) n/a 4040 20
3005.2.bw \(\chi_{3005}(89, \cdot)\) n/a 6000 20
3005.2.bx \(\chi_{3005}(4, \cdot)\) n/a 6000 20
3005.2.by \(\chi_{3005}(276, \cdot)\) n/a 3200 16
3005.2.cd \(\chi_{3005}(154, \cdot)\) n/a 4768 16
3005.2.ce \(\chi_{3005}(6, \cdot)\) n/a 8000 40
3005.2.cf \(\chi_{3005}(104, \cdot)\) n/a 11920 40
3005.2.ck \(\chi_{3005}(26, \cdot)\) n/a 8080 40
3005.2.cm \(\chi_{3005}(28, \cdot)\) n/a 9568 32
3005.2.cn \(\chi_{3005}(17, \cdot)\) n/a 9568 32
3005.2.cp \(\chi_{3005}(296, \cdot)\) n/a 8000 40
3005.2.cq \(\chi_{3005}(9, \cdot)\) n/a 12000 40
3005.2.cr \(\chi_{3005}(74, \cdot)\) n/a 12000 40
3005.2.cs \(\chi_{3005}(102, \cdot)\) n/a 23920 80
3005.2.cv \(\chi_{3005}(62, \cdot)\) n/a 23920 80
3005.2.cw \(\chi_{3005}(39, \cdot)\) n/a 23840 80
3005.2.db \(\chi_{3005}(46, \cdot)\) n/a 16000 80
3005.2.dc \(\chi_{3005}(7, \cdot)\) n/a 47840 160
3005.2.df \(\chi_{3005}(33, \cdot)\) n/a 47840 160

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3005))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3005)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(601))\)\(^{\oplus 2}\)