## Defining parameters

 Level: $$N$$ = $$2646 = 2 \cdot 3^{3} \cdot 7^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$32$$ Sturm bound: $$762048$$ Trace bound: $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2646))$$.

Total New Old
Modular forms 194112 48150 145962
Cusp forms 186913 48150 138763
Eisenstein series 7199 0 7199

## Trace form

 $$48150q + q^{2} + q^{4} - 6q^{5} - 6q^{6} - 5q^{8} - 12q^{9} + O(q^{10})$$ $$48150q + q^{2} + q^{4} - 6q^{5} - 6q^{6} - 5q^{8} - 12q^{9} - 6q^{10} - 18q^{11} - 3q^{12} - 18q^{13} - 12q^{14} - 18q^{15} - 7q^{16} - 78q^{17} + 6q^{18} - 54q^{19} - 12q^{20} - 48q^{22} - 54q^{23} - 61q^{25} - 16q^{26} + 27q^{27} - 4q^{28} - 12q^{29} + 36q^{30} - 36q^{31} + q^{32} + 27q^{33} - 6q^{34} - 36q^{35} + 6q^{36} - 52q^{37} - 13q^{38} - 42q^{39} - 6q^{40} - 102q^{41} - 76q^{43} - 78q^{47} - 6q^{48} + 20q^{49} + 199q^{50} + 216q^{51} + 78q^{52} + 504q^{53} + 180q^{54} + 342q^{55} + 279q^{57} + 246q^{58} + 609q^{59} + 198q^{60} + 222q^{61} + 464q^{62} + 252q^{63} - 5q^{64} + 846q^{65} + 288q^{66} + 274q^{67} + 345q^{68} + 378q^{69} + 132q^{70} + 480q^{71} + 24q^{72} + 366q^{73} + 386q^{74} + 372q^{75} + 111q^{76} + 156q^{77} + 180q^{78} + 124q^{79} + 12q^{80} + 30q^{82} - 60q^{83} + 24q^{85} + 2q^{86} + 36q^{87} + 3q^{88} - 159q^{89} + 18q^{90} - 76q^{91} - 48q^{92} - 6q^{93} - 66q^{94} - 258q^{95} + 6q^{96} - 132q^{97} - 72q^{98} - 36q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2646))$$

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 the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
2646.2.a $$\chi_{2646}(1, \cdot)$$ 2646.2.a.a 1 1
2646.2.a.b 1
2646.2.a.c 1
2646.2.a.d 1
2646.2.a.e 1
2646.2.a.f 1
2646.2.a.g 1
2646.2.a.h 1
2646.2.a.i 1
2646.2.a.j 1
2646.2.a.k 1
2646.2.a.l 1
2646.2.a.m 1
2646.2.a.n 1
2646.2.a.o 1
2646.2.a.p 1
2646.2.a.q 1
2646.2.a.r 1
2646.2.a.s 1
2646.2.a.t 1
2646.2.a.u 1
2646.2.a.v 1
2646.2.a.w 1
2646.2.a.x 1
2646.2.a.y 1
2646.2.a.z 1
2646.2.a.ba 1
2646.2.a.bb 1
2646.2.a.bc 1
2646.2.a.bd 1
2646.2.a.be 2
2646.2.a.bf 2
2646.2.a.bg 2
2646.2.a.bh 2
2646.2.a.bi 2
2646.2.a.bj 2
2646.2.a.bk 2
2646.2.a.bl 2
2646.2.a.bm 2
2646.2.a.bn 2
2646.2.a.bo 2
2646.2.a.bp 2
2646.2.d $$\chi_{2646}(2645, \cdot)$$ 2646.2.d.a 4 1
2646.2.d.b 4
2646.2.d.c 4
2646.2.d.d 8
2646.2.d.e 16
2646.2.d.f 16
2646.2.e $$\chi_{2646}(1549, \cdot)$$ 2646.2.e.a 2 2
2646.2.e.b 2
2646.2.e.c 2
2646.2.e.d 2
2646.2.e.e 2
2646.2.e.f 2
2646.2.e.g 2
2646.2.e.h 2
2646.2.e.i 2
2646.2.e.j 2
2646.2.e.k 4
2646.2.e.l 4
2646.2.e.m 4
2646.2.e.n 4
2646.2.e.o 6
2646.2.e.p 6
2646.2.e.q 8
2646.2.e.r 8
2646.2.e.s 8
2646.2.e.t 8
2646.2.f $$\chi_{2646}(883, \cdot)$$ 2646.2.f.a 2 2
2646.2.f.b 2
2646.2.f.c 2
2646.2.f.d 2
2646.2.f.e 2
2646.2.f.f 2
2646.2.f.g 2
2646.2.f.h 2
2646.2.f.i 2
2646.2.f.j 4
2646.2.f.k 4
2646.2.f.l 6
2646.2.f.m 6
2646.2.f.n 6
2646.2.f.o 6
2646.2.f.p 8
2646.2.f.q 8
2646.2.f.r 8
2646.2.f.s 8
2646.2.g $$\chi_{2646}(1243, \cdot)$$ n/a 108 2
2646.2.h $$\chi_{2646}(361, \cdot)$$ 2646.2.h.a 2 2
2646.2.h.b 2
2646.2.h.c 2
2646.2.h.d 2
2646.2.h.e 2
2646.2.h.f 2
2646.2.h.g 2
2646.2.h.h 2
2646.2.h.i 2
2646.2.h.j 2
2646.2.h.k 4
2646.2.h.l 4
2646.2.h.m 4
2646.2.h.n 4
2646.2.h.o 6
2646.2.h.p 6
2646.2.h.q 8
2646.2.h.r 8
2646.2.h.s 8
2646.2.h.t 8
2646.2.k $$\chi_{2646}(215, \cdot)$$ n/a 108 2
2646.2.l $$\chi_{2646}(521, \cdot)$$ 2646.2.l.a 16 2
2646.2.l.b 16
2646.2.l.c 48
2646.2.m $$\chi_{2646}(881, \cdot)$$ 2646.2.m.a 16 2
2646.2.m.b 16
2646.2.m.c 48
2646.2.t $$\chi_{2646}(1979, \cdot)$$ 2646.2.t.a 16 2
2646.2.t.b 16
2646.2.t.c 48
2646.2.u $$\chi_{2646}(379, \cdot)$$ n/a 456 6
2646.2.v $$\chi_{2646}(295, \cdot)$$ n/a 738 6
2646.2.w $$\chi_{2646}(67, \cdot)$$ n/a 720 6
2646.2.x $$\chi_{2646}(373, \cdot)$$ n/a 720 6
2646.2.y $$\chi_{2646}(377, \cdot)$$ n/a 456 6
2646.2.bd $$\chi_{2646}(293, \cdot)$$ n/a 720 6
2646.2.be $$\chi_{2646}(803, \cdot)$$ n/a 720 6
2646.2.bj $$\chi_{2646}(227, \cdot)$$ n/a 720 6
2646.2.bk $$\chi_{2646}(289, \cdot)$$ n/a 672 12
2646.2.bl $$\chi_{2646}(109, \cdot)$$ n/a 888 12
2646.2.bm $$\chi_{2646}(127, \cdot)$$ n/a 672 12
2646.2.bn $$\chi_{2646}(37, \cdot)$$ n/a 672 12
2646.2.bo $$\chi_{2646}(17, \cdot)$$ n/a 672 12
2646.2.bv $$\chi_{2646}(125, \cdot)$$ n/a 672 12
2646.2.bw $$\chi_{2646}(143, \cdot)$$ n/a 672 12
2646.2.bx $$\chi_{2646}(269, \cdot)$$ n/a 888 12
2646.2.ca $$\chi_{2646}(25, \cdot)$$ n/a 6048 36
2646.2.cb $$\chi_{2646}(193, \cdot)$$ n/a 6048 36
2646.2.cc $$\chi_{2646}(43, \cdot)$$ n/a 6048 36
2646.2.cd $$\chi_{2646}(5, \cdot)$$ n/a 6048 36
2646.2.ci $$\chi_{2646}(47, \cdot)$$ n/a 6048 36
2646.2.cj $$\chi_{2646}(41, \cdot)$$ n/a 6048 36

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2646))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2646)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(54))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(126))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(147))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(189))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(294))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(378))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(441))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(882))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1323))$$$$^{\oplus 2}$$