# Properties

 Label 234.8 Level 234 Weight 8 Dimension 2761 Nonzero newspaces 15 Sturm bound 24192 Trace bound 11

## Defining parameters

 Level: $$N$$ = $$234 = 2 \cdot 3^{2} \cdot 13$$ Weight: $$k$$ = $$8$$ Nonzero newspaces: $$15$$ Sturm bound: $$24192$$ Trace bound: $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{8}(\Gamma_1(234))$$.

Total New Old
Modular forms 10776 2761 8015
Cusp forms 10392 2761 7631
Eisenstein series 384 0 384

## Trace form

 $$2761 q - 16 q^{2} + 78 q^{3} + 640 q^{4} - 864 q^{5} - 2544 q^{6} + 3816 q^{7} + 512 q^{8} - 114 q^{9} + O(q^{10})$$ $$2761 q - 16 q^{2} + 78 q^{3} + 640 q^{4} - 864 q^{5} - 2544 q^{6} + 3816 q^{7} + 512 q^{8} - 114 q^{9} + 8424 q^{10} - 8562 q^{11} - 31202 q^{13} - 34688 q^{14} - 36720 q^{15} + 57344 q^{16} + 251109 q^{17} + 6816 q^{18} - 119184 q^{19} - 60864 q^{20} - 555708 q^{21} - 170352 q^{22} + 288720 q^{23} + 15360 q^{24} + 326671 q^{25} + 222368 q^{26} + 401760 q^{27} - 467200 q^{28} + 1576449 q^{29} + 703104 q^{30} - 380368 q^{31} - 65536 q^{32} - 3908682 q^{33} - 1803408 q^{34} + 2630424 q^{35} + 1551744 q^{36} + 4735565 q^{37} + 5137360 q^{38} + 2383176 q^{39} - 98304 q^{40} - 5843517 q^{41} - 2476224 q^{42} - 4108590 q^{43} - 3487488 q^{44} - 2894736 q^{45} - 3307392 q^{46} + 3118644 q^{47} - 319488 q^{48} + 13548898 q^{49} + 10812728 q^{50} + 1612518 q^{51} - 7678784 q^{52} - 7804956 q^{53} + 1163952 q^{54} + 1585644 q^{55} - 1187840 q^{56} - 2365602 q^{57} + 5179752 q^{58} + 8550846 q^{59} + 4119552 q^{60} - 8516251 q^{61} - 3856736 q^{62} + 16200408 q^{63} - 9175040 q^{64} + 30254253 q^{65} + 8045568 q^{66} + 18420270 q^{67} - 4056384 q^{68} - 44123904 q^{69} + 8057760 q^{70} - 50253192 q^{71} - 4641792 q^{72} - 16563444 q^{73} - 1160600 q^{74} + 79317918 q^{75} - 16609152 q^{76} + 24867132 q^{77} + 6015408 q^{78} + 30235976 q^{79} - 1241088 q^{80} - 23201178 q^{81} + 65561160 q^{82} + 4857720 q^{83} + 17939712 q^{84} - 75060183 q^{85} + 10270192 q^{86} - 102640884 q^{87} - 10902528 q^{88} - 143598672 q^{89} - 93851136 q^{90} + 36386772 q^{91} + 5447424 q^{92} + 123213024 q^{93} + 20174976 q^{94} + 57970344 q^{95} + 9437184 q^{96} + 18883730 q^{97} + 125249184 q^{98} - 200230596 q^{99} + O(q^{100})$$

## Decomposition of $$S_{8}^{\mathrm{new}}(\Gamma_1(234))$$

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
234.8.a $$\chi_{234}(1, \cdot)$$ 234.8.a.a 1 1
234.8.a.b 1
234.8.a.c 1
234.8.a.d 1
234.8.a.e 1
234.8.a.f 2
234.8.a.g 2
234.8.a.h 2
234.8.a.i 2
234.8.a.j 2
234.8.a.k 2
234.8.a.l 2
234.8.a.m 2
234.8.a.n 3
234.8.a.o 3
234.8.a.p 4
234.8.a.q 4
234.8.b $$\chi_{234}(181, \cdot)$$ 234.8.b.a 6 1
234.8.b.b 8
234.8.b.c 10
234.8.b.d 16
234.8.e $$\chi_{234}(79, \cdot)$$ n/a 168 2
234.8.f $$\chi_{234}(133, \cdot)$$ n/a 196 2
234.8.g $$\chi_{234}(61, \cdot)$$ n/a 196 2
234.8.h $$\chi_{234}(55, \cdot)$$ 234.8.h.a 6 2
234.8.h.b 8
234.8.h.c 8
234.8.h.d 8
234.8.h.e 10
234.8.h.f 10
234.8.h.g 16
234.8.h.h 16
234.8.j $$\chi_{234}(125, \cdot)$$ 234.8.j.a 28 2
234.8.j.b 32
234.8.l $$\chi_{234}(127, \cdot)$$ 234.8.l.a 16 2
234.8.l.b 16
234.8.l.c 16
234.8.l.d 36
234.8.p $$\chi_{234}(43, \cdot)$$ n/a 196 2
234.8.s $$\chi_{234}(121, \cdot)$$ n/a 196 2
234.8.t $$\chi_{234}(25, \cdot)$$ n/a 196 2
234.8.x $$\chi_{234}(71, \cdot)$$ n/a 136 4
234.8.y $$\chi_{234}(11, \cdot)$$ n/a 392 4
234.8.z $$\chi_{234}(41, \cdot)$$ n/a 392 4
234.8.bd $$\chi_{234}(5, \cdot)$$ n/a 392 4

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

## Decomposition of $$S_{8}^{\mathrm{old}}(\Gamma_1(234))$$ into lower level spaces

$$S_{8}^{\mathrm{old}}(\Gamma_1(234)) \cong$$ $$S_{8}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 12}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 6}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 8}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 4}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 4}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 6}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 2}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 3}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 4}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(78))$$$$^{\oplus 2}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(117))$$$$^{\oplus 2}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(234))$$$$^{\oplus 1}$$