## Defining parameters

 Level: $$N$$ = $$2366 = 2 \cdot 7 \cdot 13^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$30$$ Sturm bound: $$681408$$ Trace bound: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2366))$$.

Total New Old
Modular forms 173088 53774 119314
Cusp forms 167617 53774 113843
Eisenstein series 5471 0 5471

## Trace form

 $$53774q - 2q^{2} - 6q^{3} - 6q^{5} - 2q^{6} + 8q^{7} + 10q^{8} + 52q^{9} + O(q^{10})$$ $$53774q - 2q^{2} - 6q^{3} - 6q^{5} - 2q^{6} + 8q^{7} + 10q^{8} + 52q^{9} + 54q^{10} + 36q^{11} + 10q^{12} + 48q^{13} + 22q^{14} + 72q^{15} + 16q^{16} + 48q^{17} + 46q^{18} + 94q^{19} + 6q^{20} + 50q^{21} - 12q^{22} + 24q^{23} - 2q^{24} + 24q^{25} + 108q^{27} + 8q^{28} + 120q^{29} + 72q^{30} + 124q^{31} - 2q^{32} + 192q^{33} + 72q^{34} + 138q^{35} + 84q^{36} + 88q^{37} + 122q^{38} + 104q^{39} - 6q^{40} + 168q^{41} + 70q^{42} + 140q^{43} + 84q^{44} + 222q^{45} + 72q^{46} + 132q^{47} - 6q^{48} + 64q^{49} + 82q^{50} + 204q^{51} + 14q^{52} + 96q^{53} + 100q^{54} + 168q^{55} + 22q^{56} + 172q^{57} + 84q^{58} + 126q^{59} + 72q^{60} + 102q^{61} + 116q^{62} + 236q^{63} + 12q^{64} + 174q^{65} + 144q^{66} + 232q^{67} + 384q^{69} + 66q^{70} + 216q^{71} + 82q^{72} + 232q^{73} - 28q^{74} + 142q^{75} - 98q^{76} - 204q^{77} - 24q^{78} - 264q^{79} + 6q^{80} - 260q^{81} - 420q^{82} - 138q^{83} - 286q^{84} - 480q^{85} - 244q^{86} - 492q^{87} - 12q^{88} - 288q^{89} - 558q^{90} - 236q^{91} - 216q^{92} - 296q^{93} - 516q^{94} - 408q^{95} - 2q^{96} - 572q^{97} - 194q^{98} - 588q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2366))$$

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
2366.2.a $$\chi_{2366}(1, \cdot)$$ 2366.2.a.a 1 1
2366.2.a.b 1
2366.2.a.c 1
2366.2.a.d 1
2366.2.a.e 1
2366.2.a.f 1
2366.2.a.g 1
2366.2.a.h 1
2366.2.a.i 1
2366.2.a.j 1
2366.2.a.k 1
2366.2.a.l 1
2366.2.a.m 1
2366.2.a.n 1
2366.2.a.o 1
2366.2.a.p 1
2366.2.a.q 2
2366.2.a.r 2
2366.2.a.s 2
2366.2.a.t 2
2366.2.a.u 3
2366.2.a.v 3
2366.2.a.w 3
2366.2.a.x 3
2366.2.a.y 3
2366.2.a.z 3
2366.2.a.ba 3
2366.2.a.bb 3
2366.2.a.bc 3
2366.2.a.bd 3
2366.2.a.be 6
2366.2.a.bf 6
2366.2.a.bg 6
2366.2.a.bh 6
2366.2.d $$\chi_{2366}(337, \cdot)$$ 2366.2.d.a 2 1
2366.2.d.b 2
2366.2.d.c 2
2366.2.d.d 2
2366.2.d.e 2
2366.2.d.f 2
2366.2.d.g 2
2366.2.d.h 2
2366.2.d.i 2
2366.2.d.j 2
2366.2.d.k 4
2366.2.d.l 4
2366.2.d.m 6
2366.2.d.n 6
2366.2.d.o 6
2366.2.d.p 6
2366.2.d.q 12
2366.2.d.r 12
2366.2.e $$\chi_{2366}(529, \cdot)$$ n/a 204 2
2366.2.f $$\chi_{2366}(1353, \cdot)$$ n/a 208 2
2366.2.g $$\chi_{2366}(1205, \cdot)$$ n/a 156 2
2366.2.h $$\chi_{2366}(191, \cdot)$$ n/a 204 2
2366.2.i $$\chi_{2366}(2127, \cdot)$$ n/a 200 2
2366.2.m $$\chi_{2366}(1037, \cdot)$$ n/a 152 2
2366.2.n $$\chi_{2366}(1689, \cdot)$$ n/a 208 2
2366.2.o $$\chi_{2366}(23, \cdot)$$ n/a 204 2
2366.2.v $$\chi_{2366}(361, \cdot)$$ n/a 204 2
2366.2.w $$\chi_{2366}(19, \cdot)$$ n/a 408 4
2366.2.ba $$\chi_{2366}(587, \cdot)$$ n/a 416 4
2366.2.bb $$\chi_{2366}(437, \cdot)$$ n/a 416 4
2366.2.bc $$\chi_{2366}(89, \cdot)$$ n/a 408 4
2366.2.be $$\chi_{2366}(183, \cdot)$$ n/a 1080 12
2366.2.bf $$\chi_{2366}(155, \cdot)$$ n/a 1104 12
2366.2.bi $$\chi_{2366}(9, \cdot)$$ n/a 2928 24
2366.2.bj $$\chi_{2366}(29, \cdot)$$ n/a 2160 24
2366.2.bk $$\chi_{2366}(53, \cdot)$$ n/a 2880 24
2366.2.bl $$\chi_{2366}(107, \cdot)$$ n/a 2928 24
2366.2.bn $$\chi_{2366}(83, \cdot)$$ n/a 2976 24
2366.2.bo $$\chi_{2366}(121, \cdot)$$ n/a 2928 24
2366.2.bv $$\chi_{2366}(95, \cdot)$$ n/a 2928 24
2366.2.bw $$\chi_{2366}(25, \cdot)$$ n/a 2880 24
2366.2.bx $$\chi_{2366}(43, \cdot)$$ n/a 2208 24
2366.2.cb $$\chi_{2366}(45, \cdot)$$ n/a 5856 48
2366.2.cc $$\chi_{2366}(5, \cdot)$$ n/a 5760 48
2366.2.cd $$\chi_{2366}(41, \cdot)$$ n/a 5760 48
2366.2.ch $$\chi_{2366}(33, \cdot)$$ n/a 5856 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2366))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2366)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(91))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(169))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(182))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(338))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1183))$$$$^{\oplus 2}$$