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Properties

Label 2013.4
Level 2013
Weight 4
Dimension 327980
Nonzero newspaces 84
Sturm bound 1190400
Trace bound 16

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Defining parameters

Level: \( N \) = \( 2013 = 3 \cdot 11 \cdot 61 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 84 \)
Sturm bound: \(1190400\)
Trace bound: \(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2013))\).

Total New Old
Modular forms 448800 330100 118700
Cusp forms 444000 327980 116020
Eisenstein series 4800 2120 2680

Trace form

\( 327980 q - 230 q^{3} - 460 q^{4} - 330 q^{6} - 500 q^{7} + 160 q^{8} - 70 q^{9} + O(q^{10}) \) \( 327980 q - 230 q^{3} - 460 q^{4} - 330 q^{6} - 500 q^{7} + 160 q^{8} - 70 q^{9} - 80 q^{10} + 200 q^{11} - 200 q^{12} - 380 q^{13} - 780 q^{14} - 850 q^{15} - 1980 q^{16} - 600 q^{17} - 510 q^{18} + 440 q^{19} + 1900 q^{20} + 600 q^{21} + 2000 q^{22} + 760 q^{23} + 1790 q^{24} + 260 q^{25} + 100 q^{26} - 290 q^{27} - 2560 q^{28} - 1400 q^{29} - 4100 q^{30} - 3220 q^{31} - 3560 q^{32} - 3870 q^{33} - 4800 q^{34} - 2320 q^{35} - 2670 q^{36} - 380 q^{37} + 1300 q^{38} + 1910 q^{39} + 2600 q^{40} + 4440 q^{41} + 4640 q^{42} - 160 q^{43} + 1540 q^{44} + 4820 q^{45} + 3120 q^{46} - 12280 q^{47} - 15300 q^{48} - 16660 q^{49} - 12140 q^{50} - 1740 q^{51} - 6480 q^{52} - 160 q^{53} + 840 q^{54} + 3880 q^{55} + 28080 q^{56} + 9600 q^{57} + 28840 q^{58} + 15960 q^{59} + 22120 q^{60} + 29570 q^{61} + 36240 q^{62} - 7410 q^{63} + 33620 q^{64} + 2880 q^{65} - 10950 q^{66} + 920 q^{67} - 6880 q^{68} - 9740 q^{69} - 32280 q^{70} - 9720 q^{71} - 12980 q^{72} - 34420 q^{73} - 40500 q^{74} - 19080 q^{75} - 64480 q^{76} - 10920 q^{77} + 14140 q^{78} + 6740 q^{79} + 19620 q^{80} + 15410 q^{81} + 25060 q^{82} + 15440 q^{83} + 22920 q^{84} + 24340 q^{85} + 11920 q^{86} + 10200 q^{87} + 22040 q^{88} + 7000 q^{89} - 15440 q^{90} - 4860 q^{91} - 22100 q^{92} - 12450 q^{93} - 26560 q^{94} - 7200 q^{95} - 28520 q^{96} - 12400 q^{97} - 10120 q^{98} - 10000 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2013))\)

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
2013.4.a \(\chi_{2013}(1, \cdot)\) 2013.4.a.a 36 1
2013.4.a.b 36
2013.4.a.c 37
2013.4.a.d 37
2013.4.a.e 38
2013.4.a.f 38
2013.4.a.g 39
2013.4.a.h 39
2013.4.b \(\chi_{2013}(2012, \cdot)\) n/a 740 1
2013.4.e \(\chi_{2013}(1585, \cdot)\) n/a 308 1
2013.4.f \(\chi_{2013}(428, \cdot)\) n/a 720 1
2013.4.i \(\chi_{2013}(562, \cdot)\) n/a 624 2
2013.4.j \(\chi_{2013}(538, \cdot)\) n/a 744 2
2013.4.m \(\chi_{2013}(782, \cdot)\) n/a 1240 2
2013.4.n \(\chi_{2013}(70, \cdot)\) n/a 1488 4
2013.4.o \(\chi_{2013}(34, \cdot)\) n/a 1248 4
2013.4.p \(\chi_{2013}(367, \cdot)\) n/a 1440 4
2013.4.q \(\chi_{2013}(58, \cdot)\) n/a 1488 4
2013.4.r \(\chi_{2013}(1522, \cdot)\) n/a 1488 4
2013.4.s \(\chi_{2013}(400, \cdot)\) n/a 1488 4
2013.4.v \(\chi_{2013}(230, \cdot)\) n/a 1480 2
2013.4.w \(\chi_{2013}(1024, \cdot)\) n/a 616 2
2013.4.z \(\chi_{2013}(197, \cdot)\) n/a 1480 2
2013.4.ba \(\chi_{2013}(163, \cdot)\) n/a 1488 4
2013.4.bd \(\chi_{2013}(1040, \cdot)\) n/a 2960 4
2013.4.bf \(\chi_{2013}(314, \cdot)\) n/a 2960 4
2013.4.bl \(\chi_{2013}(497, \cdot)\) n/a 2960 4
2013.4.bn \(\chi_{2013}(62, \cdot)\) n/a 2880 4
2013.4.bo \(\chi_{2013}(131, \cdot)\) n/a 2960 4
2013.4.bq \(\chi_{2013}(1559, \cdot)\) n/a 2960 4
2013.4.bu \(\chi_{2013}(41, \cdot)\) n/a 2960 4
2013.4.bv \(\chi_{2013}(895, \cdot)\) n/a 1488 4
2013.4.bx \(\chi_{2013}(487, \cdot)\) n/a 1488 4
2013.4.ca \(\chi_{2013}(64, \cdot)\) n/a 1488 4
2013.4.cc \(\chi_{2013}(430, \cdot)\) n/a 1232 4
2013.4.cd \(\chi_{2013}(296, \cdot)\) n/a 2960 4
2013.4.cf \(\chi_{2013}(1064, \cdot)\) n/a 2960 4
2013.4.ci \(\chi_{2013}(182, \cdot)\) n/a 2960 4
2013.4.ck \(\chi_{2013}(149, \cdot)\) n/a 2960 4
2013.4.cl \(\chi_{2013}(796, \cdot)\) n/a 1488 4
2013.4.cp \(\chi_{2013}(95, \cdot)\) n/a 2960 4
2013.4.cq \(\chi_{2013}(650, \cdot)\) n/a 2480 4
2013.4.ct \(\chi_{2013}(406, \cdot)\) n/a 1488 4
2013.4.cu \(\chi_{2013}(757, \cdot)\) n/a 2976 8
2013.4.cv \(\chi_{2013}(25, \cdot)\) n/a 2976 8
2013.4.cw \(\chi_{2013}(361, \cdot)\) n/a 2976 8
2013.4.cx \(\chi_{2013}(169, \cdot)\) n/a 2976 8
2013.4.cy \(\chi_{2013}(199, \cdot)\) n/a 2496 8
2013.4.cz \(\chi_{2013}(16, \cdot)\) n/a 2976 8
2013.4.da \(\chi_{2013}(191, \cdot)\) n/a 5920 8
2013.4.dd \(\chi_{2013}(28, \cdot)\) n/a 2976 8
2013.4.df \(\chi_{2013}(85, \cdot)\) n/a 2976 8
2013.4.dh \(\chi_{2013}(236, \cdot)\) n/a 5920 8
2013.4.di \(\chi_{2013}(389, \cdot)\) n/a 5920 8
2013.4.dj \(\chi_{2013}(377, \cdot)\) n/a 5920 8
2013.4.dn \(\chi_{2013}(23, \cdot)\) n/a 4960 8
2013.4.do \(\chi_{2013}(175, \cdot)\) n/a 2976 8
2013.4.ds \(\chi_{2013}(172, \cdot)\) n/a 2976 8
2013.4.dt \(\chi_{2013}(211, \cdot)\) n/a 2976 8
2013.4.du \(\chi_{2013}(145, \cdot)\) n/a 2976 8
2013.4.dw \(\chi_{2013}(38, \cdot)\) n/a 5920 8
2013.4.dy \(\chi_{2013}(83, \cdot)\) n/a 5920 8
2013.4.ec \(\chi_{2013}(202, \cdot)\) n/a 2976 8
2013.4.ed \(\chi_{2013}(431, \cdot)\) n/a 5920 8
2013.4.ef \(\chi_{2013}(380, \cdot)\) n/a 5920 8
2013.4.ei \(\chi_{2013}(107, \cdot)\) n/a 5920 8
2013.4.ek \(\chi_{2013}(65, \cdot)\) n/a 5920 8
2013.4.el \(\chi_{2013}(100, \cdot)\) n/a 2464 8
2013.4.en \(\chi_{2013}(4, \cdot)\) n/a 2976 8
2013.4.eq \(\chi_{2013}(136, \cdot)\) n/a 2976 8
2013.4.es \(\chi_{2013}(49, \cdot)\) n/a 2976 8
2013.4.et \(\chi_{2013}(161, \cdot)\) n/a 5920 8
2013.4.ex \(\chi_{2013}(266, \cdot)\) n/a 5920 8
2013.4.ez \(\chi_{2013}(164, \cdot)\) n/a 5920 8
2013.4.fa \(\chi_{2013}(74, \cdot)\) n/a 5920 8
2013.4.fc \(\chi_{2013}(260, \cdot)\) n/a 5920 8
2013.4.fi \(\chi_{2013}(134, \cdot)\) n/a 5920 8
2013.4.fk \(\chi_{2013}(167, \cdot)\) n/a 5920 8
2013.4.fn \(\chi_{2013}(97, \cdot)\) n/a 2976 8
2013.4.fp \(\chi_{2013}(26, \cdot)\) n/a 11840 16
2013.4.fr \(\chi_{2013}(7, \cdot)\) n/a 5952 16
2013.4.fs \(\chi_{2013}(40, \cdot)\) n/a 5952 16
2013.4.ft \(\chi_{2013}(139, \cdot)\) n/a 5952 16
2013.4.fx \(\chi_{2013}(10, \cdot)\) n/a 5952 16
2013.4.fy \(\chi_{2013}(254, \cdot)\) n/a 9920 16
2013.4.gc \(\chi_{2013}(185, \cdot)\) n/a 11840 16
2013.4.gd \(\chi_{2013}(212, \cdot)\) n/a 11840 16
2013.4.ge \(\chi_{2013}(71, \cdot)\) n/a 11840 16
2013.4.gg \(\chi_{2013}(79, \cdot)\) n/a 5952 16
2013.4.gi \(\chi_{2013}(250, \cdot)\) n/a 5952 16
2013.4.gl \(\chi_{2013}(152, \cdot)\) n/a 11840 16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2013))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2013)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(61))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(183))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(671))\)\(^{\oplus 2}\)