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Properties

Label 2574.2
Level 2574
Weight 2
Dimension 46520
Nonzero newspaces 60
Sturm bound 725760
Trace bound 27

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Defining parameters

Level: \( N \) = \( 2574 = 2 \cdot 3^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(725760\)
Trace bound: \(27\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2574))\).

Total New Old
Modular forms 185280 46520 138760
Cusp forms 177601 46520 131081
Eisenstein series 7679 0 7679

Trace form

\( 46520 q - 4 q^{2} - 12 q^{3} - 4 q^{4} + 12 q^{6} - 36 q^{7} + 2 q^{8} + 12 q^{9} + O(q^{10}) \) \( 46520 q - 4 q^{2} - 12 q^{3} - 4 q^{4} + 12 q^{6} - 36 q^{7} + 2 q^{8} + 12 q^{9} - 50 q^{10} - 26 q^{11} - 62 q^{13} - 52 q^{14} - 12 q^{16} - 94 q^{17} - 24 q^{18} - 94 q^{19} - 6 q^{20} + 24 q^{21} + 6 q^{22} + 40 q^{23} + 8 q^{24} + 70 q^{25} + 68 q^{26} + 120 q^{27} + 100 q^{28} + 250 q^{29} + 216 q^{30} + 260 q^{31} + 26 q^{32} + 254 q^{33} + 276 q^{34} + 616 q^{35} + 128 q^{36} + 250 q^{37} + 400 q^{38} + 252 q^{39} + 60 q^{40} + 406 q^{41} + 224 q^{42} + 200 q^{43} + 70 q^{44} + 280 q^{45} + 56 q^{46} + 136 q^{47} + 12 q^{48} + 52 q^{49} + 118 q^{50} + 152 q^{51} - 6 q^{52} + 84 q^{53} + 36 q^{54} - 40 q^{55} - 32 q^{56} + 172 q^{57} - 158 q^{58} + 42 q^{59} - 90 q^{61} - 164 q^{62} + 208 q^{63} + 2 q^{64} + 174 q^{65} + 160 q^{67} - 34 q^{68} + 304 q^{69} - 152 q^{70} + 304 q^{71} + 12 q^{72} + 336 q^{73} - 102 q^{74} + 320 q^{75} - 72 q^{76} + 244 q^{77} - 12 q^{78} + 76 q^{79} - 26 q^{80} + 76 q^{81} + 20 q^{82} + 30 q^{83} - 184 q^{84} + 78 q^{85} - 314 q^{86} - 136 q^{87} - 14 q^{88} - 216 q^{89} - 400 q^{90} + 196 q^{91} - 204 q^{92} - 256 q^{93} - 56 q^{94} - 492 q^{95} - 170 q^{97} - 486 q^{98} - 748 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2574))\)

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
2574.2.a \(\chi_{2574}(1, \cdot)\) 2574.2.a.a 1 1
2574.2.a.b 1
2574.2.a.c 1
2574.2.a.d 1
2574.2.a.e 1
2574.2.a.f 1
2574.2.a.g 1
2574.2.a.h 1
2574.2.a.i 1
2574.2.a.j 1
2574.2.a.k 1
2574.2.a.l 1
2574.2.a.m 1
2574.2.a.n 1
2574.2.a.o 1
2574.2.a.p 1
2574.2.a.q 1
2574.2.a.r 1
2574.2.a.s 1
2574.2.a.t 1
2574.2.a.u 1
2574.2.a.v 1
2574.2.a.w 1
2574.2.a.x 1
2574.2.a.y 1
2574.2.a.z 2
2574.2.a.ba 2
2574.2.a.bb 2
2574.2.a.bc 2
2574.2.a.bd 2
2574.2.a.be 2
2574.2.a.bf 2
2574.2.a.bg 2
2574.2.a.bh 3
2574.2.a.bi 3
2574.2.a.bj 3
2574.2.b \(\chi_{2574}(989, \cdot)\) 2574.2.b.a 4 1
2574.2.b.b 4
2574.2.b.c 20
2574.2.b.d 20
2574.2.c \(\chi_{2574}(1585, \cdot)\) 2574.2.c.a 2 1
2574.2.c.b 2
2574.2.c.c 2
2574.2.c.d 2
2574.2.c.e 2
2574.2.c.f 4
2574.2.c.g 4
2574.2.c.h 4
2574.2.c.i 8
2574.2.c.j 8
2574.2.c.k 8
2574.2.c.l 8
2574.2.c.m 8
2574.2.h \(\chi_{2574}(2573, \cdot)\) 2574.2.h.a 4 1
2574.2.h.b 4
2574.2.h.c 16
2574.2.h.d 32
2574.2.i \(\chi_{2574}(133, \cdot)\) n/a 280 2
2574.2.j \(\chi_{2574}(859, \cdot)\) n/a 240 2
2574.2.k \(\chi_{2574}(529, \cdot)\) n/a 280 2
2574.2.l \(\chi_{2574}(991, \cdot)\) n/a 112 2
2574.2.o \(\chi_{2574}(109, \cdot)\) n/a 140 2
2574.2.p \(\chi_{2574}(2267, \cdot)\) n/a 104 2
2574.2.q \(\chi_{2574}(235, \cdot)\) n/a 240 4
2574.2.t \(\chi_{2574}(199, \cdot)\) n/a 116 2
2574.2.u \(\chi_{2574}(1979, \cdot)\) n/a 112 2
2574.2.x \(\chi_{2574}(329, \cdot)\) n/a 336 2
2574.2.y \(\chi_{2574}(857, \cdot)\) n/a 336 2
2574.2.bd \(\chi_{2574}(725, \cdot)\) n/a 336 2
2574.2.be \(\chi_{2574}(659, \cdot)\) n/a 336 2
2574.2.bf \(\chi_{2574}(1453, \cdot)\) n/a 280 2
2574.2.bk \(\chi_{2574}(1057, \cdot)\) n/a 280 2
2574.2.bl \(\chi_{2574}(263, \cdot)\) n/a 336 2
2574.2.bm \(\chi_{2574}(727, \cdot)\) n/a 280 2
2574.2.bn \(\chi_{2574}(131, \cdot)\) n/a 288 2
2574.2.bq \(\chi_{2574}(1187, \cdot)\) n/a 112 2
2574.2.bt \(\chi_{2574}(233, \cdot)\) n/a 224 4
2574.2.by \(\chi_{2574}(755, \cdot)\) n/a 192 4
2574.2.bz \(\chi_{2574}(181, \cdot)\) n/a 280 4
2574.2.cc \(\chi_{2574}(241, \cdot)\) n/a 672 4
2574.2.cd \(\chi_{2574}(89, \cdot)\) n/a 176 4
2574.2.ce \(\chi_{2574}(353, \cdot)\) n/a 560 4
2574.2.cf \(\chi_{2574}(505, \cdot)\) n/a 280 4
2574.2.cg \(\chi_{2574}(175, \cdot)\) n/a 672 4
2574.2.ch \(\chi_{2574}(1211, \cdot)\) n/a 560 4
2574.2.co \(\chi_{2574}(551, \cdot)\) n/a 560 4
2574.2.cp \(\chi_{2574}(967, \cdot)\) n/a 672 4
2574.2.cq \(\chi_{2574}(289, \cdot)\) n/a 560 8
2574.2.cr \(\chi_{2574}(295, \cdot)\) n/a 1344 8
2574.2.cs \(\chi_{2574}(157, \cdot)\) n/a 1152 8
2574.2.ct \(\chi_{2574}(367, \cdot)\) n/a 1344 8
2574.2.cu \(\chi_{2574}(73, \cdot)\) n/a 560 8
2574.2.cv \(\chi_{2574}(125, \cdot)\) n/a 448 8
2574.2.da \(\chi_{2574}(17, \cdot)\) n/a 448 8
2574.2.dd \(\chi_{2574}(25, \cdot)\) n/a 1344 8
2574.2.de \(\chi_{2574}(365, \cdot)\) n/a 1152 8
2574.2.df \(\chi_{2574}(355, \cdot)\) n/a 1344 8
2574.2.dg \(\chi_{2574}(29, \cdot)\) n/a 1344 8
2574.2.dl \(\chi_{2574}(425, \cdot)\) n/a 1344 8
2574.2.dm \(\chi_{2574}(49, \cdot)\) n/a 1344 8
2574.2.dn \(\chi_{2574}(173, \cdot)\) n/a 1344 8
2574.2.ds \(\chi_{2574}(545, \cdot)\) n/a 1344 8
2574.2.dt \(\chi_{2574}(95, \cdot)\) n/a 1344 8
2574.2.dw \(\chi_{2574}(361, \cdot)\) n/a 560 8
2574.2.dx \(\chi_{2574}(35, \cdot)\) n/a 448 8
2574.2.ea \(\chi_{2574}(5, \cdot)\) n/a 2688 16
2574.2.eb \(\chi_{2574}(151, \cdot)\) n/a 2688 16
2574.2.ei \(\chi_{2574}(7, \cdot)\) n/a 2688 16
2574.2.ej \(\chi_{2574}(59, \cdot)\) n/a 2688 16
2574.2.ek \(\chi_{2574}(71, \cdot)\) n/a 896 16
2574.2.el \(\chi_{2574}(85, \cdot)\) n/a 2688 16
2574.2.em \(\chi_{2574}(19, \cdot)\) n/a 1120 16
2574.2.en \(\chi_{2574}(137, \cdot)\) n/a 2688 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2574))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2574)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(143))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(234))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(286))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(429))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(858))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1287))\)\(^{\oplus 2}\)