# Properties

 Label 1078.4 Level 1078 Weight 4 Dimension 33291 Nonzero newspaces 16 Sturm bound 282240 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$1078 = 2 \cdot 7^{2} \cdot 11$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$16$$ Sturm bound: $$282240$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(1078))$$.

Total New Old
Modular forms 107040 33291 73749
Cusp forms 104640 33291 71349
Eisenstein series 2400 0 2400

## Trace form

 $$33291 q + 48 q^{3} - 96 q^{5} - 94 q^{6} - 96 q^{7} + 8 q^{9} + O(q^{10})$$ $$33291 q + 48 q^{3} - 96 q^{5} - 94 q^{6} - 96 q^{7} + 8 q^{9} + 44 q^{10} - 16 q^{11} + 112 q^{12} + 224 q^{13} + 264 q^{14} + 362 q^{15} - 290 q^{17} - 442 q^{18} - 465 q^{19} - 480 q^{20} - 144 q^{21} - 432 q^{22} - 786 q^{23} + 8 q^{24} + 1140 q^{25} + 1592 q^{26} + 2379 q^{27} + 240 q^{28} + 2054 q^{29} - 108 q^{30} + 930 q^{31} - 160 q^{32} - 2405 q^{33} - 2232 q^{34} - 840 q^{35} - 772 q^{36} - 9480 q^{37} - 4836 q^{38} - 9400 q^{39} - 1200 q^{40} - 3682 q^{41} + 1656 q^{42} + 3650 q^{43} + 2572 q^{44} + 16718 q^{45} + 10272 q^{46} + 7406 q^{47} + 960 q^{48} + 15948 q^{49} + 7144 q^{50} + 17953 q^{51} + 1296 q^{52} + 10172 q^{53} + 1800 q^{54} + 3554 q^{55} - 576 q^{56} - 3729 q^{57} - 10752 q^{58} - 13297 q^{59} - 9552 q^{60} - 37228 q^{61} - 25476 q^{62} - 37320 q^{63} + 1536 q^{64} - 27464 q^{65} - 14168 q^{66} - 10772 q^{67} - 680 q^{68} + 6672 q^{69} + 4608 q^{70} + 15672 q^{71} + 9632 q^{72} + 19794 q^{73} + 21448 q^{74} + 66931 q^{75} + 14216 q^{76} + 15906 q^{77} + 37168 q^{78} + 29640 q^{79} + 5504 q^{80} + 27201 q^{81} + 8794 q^{82} - 2323 q^{83} + 576 q^{84} - 4612 q^{85} + 770 q^{86} - 12152 q^{87} - 3472 q^{88} - 5410 q^{89} - 38388 q^{90} - 13068 q^{91} - 3408 q^{92} - 24346 q^{93} - 32464 q^{94} - 11776 q^{95} - 768 q^{96} - 3945 q^{97} - 5280 q^{98} + 706 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(1078))$$

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
1078.4.a $$\chi_{1078}(1, \cdot)$$ 1078.4.a.a 1 1
1078.4.a.b 1
1078.4.a.c 1
1078.4.a.d 1
1078.4.a.e 1
1078.4.a.f 1
1078.4.a.g 1
1078.4.a.h 1
1078.4.a.i 2
1078.4.a.j 2
1078.4.a.k 2
1078.4.a.l 2
1078.4.a.m 2
1078.4.a.n 2
1078.4.a.o 2
1078.4.a.p 3
1078.4.a.q 4
1078.4.a.r 4
1078.4.a.s 4
1078.4.a.t 5
1078.4.a.u 5
1078.4.a.v 5
1078.4.a.w 5
1078.4.a.x 5
1078.4.a.y 5
1078.4.a.z 5
1078.4.a.ba 5
1078.4.a.bb 8
1078.4.a.bc 8
1078.4.a.bd 10
1078.4.c $$\chi_{1078}(1077, \cdot)$$ n/a 120 1
1078.4.e $$\chi_{1078}(67, \cdot)$$ n/a 200 2
1078.4.f $$\chi_{1078}(295, \cdot)$$ n/a 492 4
1078.4.i $$\chi_{1078}(901, \cdot)$$ n/a 240 2
1078.4.j $$\chi_{1078}(155, \cdot)$$ n/a 840 6
1078.4.l $$\chi_{1078}(195, \cdot)$$ n/a 480 4
1078.4.o $$\chi_{1078}(153, \cdot)$$ n/a 1008 6
1078.4.q $$\chi_{1078}(361, \cdot)$$ n/a 960 8
1078.4.r $$\chi_{1078}(23, \cdot)$$ n/a 1680 12
1078.4.s $$\chi_{1078}(19, \cdot)$$ n/a 960 8
1078.4.v $$\chi_{1078}(15, \cdot)$$ n/a 4032 24
1078.4.w $$\chi_{1078}(87, \cdot)$$ n/a 2016 12
1078.4.ba $$\chi_{1078}(13, \cdot)$$ n/a 4032 24
1078.4.bc $$\chi_{1078}(9, \cdot)$$ n/a 8064 48
1078.4.bf $$\chi_{1078}(17, \cdot)$$ n/a 8064 48

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(1078))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(1078)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(154))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(539))$$$$^{\oplus 2}$$