## Defining parameters

 Level: $$N$$ = $$3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$32$$ Sturm bound: $$1128960$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(3234))$$.

Total New Old
Modular forms 287040 66584 220456
Cusp forms 277441 66584 210857
Eisenstein series 9599 0 9599

## Trace form

 $$66584 q + 2 q^{2} - 6 q^{3} - 14 q^{4} - 36 q^{5} - 27 q^{6} - 32 q^{7} + 2 q^{8} - 50 q^{9} + O(q^{10})$$ $$66584 q + 2 q^{2} - 6 q^{3} - 14 q^{4} - 36 q^{5} - 27 q^{6} - 32 q^{7} + 2 q^{8} - 50 q^{9} - 56 q^{10} - 56 q^{11} - 16 q^{12} - 56 q^{13} - 18 q^{15} + 2 q^{16} - 52 q^{17} + 45 q^{18} - 54 q^{19} + 12 q^{20} + 20 q^{21} + 12 q^{22} - 20 q^{23} + 31 q^{24} - 74 q^{25} - 20 q^{26} + 24 q^{27} - 24 q^{28} - 56 q^{29} - 6 q^{30} - 116 q^{31} + 2 q^{32} + 9 q^{33} - 60 q^{34} - 96 q^{35} - 25 q^{36} + 76 q^{37} + 64 q^{38} + 122 q^{39} + 132 q^{40} + 208 q^{41} + 108 q^{42} + 44 q^{43} + 28 q^{44} + 132 q^{45} + 320 q^{46} + 208 q^{47} + 22 q^{48} + 576 q^{49} + 166 q^{50} + 365 q^{51} + 76 q^{52} + 240 q^{53} + 64 q^{54} + 320 q^{55} + 144 q^{56} + 91 q^{57} + 364 q^{58} + 204 q^{59} + 124 q^{60} + 496 q^{61} + 316 q^{62} + 240 q^{63} - 14 q^{64} + 432 q^{65} + 432 q^{66} + 420 q^{67} + 188 q^{68} + 522 q^{69} + 360 q^{70} + 736 q^{71} + 174 q^{72} + 580 q^{73} + 372 q^{74} + 825 q^{75} + 196 q^{76} + 252 q^{77} + 372 q^{78} + 340 q^{79} + 184 q^{80} + 866 q^{81} + 266 q^{82} + 684 q^{83} + 68 q^{84} + 684 q^{85} + 508 q^{86} + 756 q^{87} + 208 q^{88} + 552 q^{89} + 454 q^{90} + 472 q^{91} - 48 q^{92} + 786 q^{93} + 88 q^{94} + 660 q^{95} + 26 q^{96} + 102 q^{97} - 48 q^{98} + 210 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(3234))$$

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
3234.2.a $$\chi_{3234}(1, \cdot)$$ 3234.2.a.a 1 1
3234.2.a.b 1
3234.2.a.c 1
3234.2.a.d 1
3234.2.a.e 1
3234.2.a.f 1
3234.2.a.g 1
3234.2.a.h 1
3234.2.a.i 1
3234.2.a.j 1
3234.2.a.k 1
3234.2.a.l 1
3234.2.a.m 1
3234.2.a.n 1
3234.2.a.o 1
3234.2.a.p 1
3234.2.a.q 1
3234.2.a.r 1
3234.2.a.s 1
3234.2.a.t 1
3234.2.a.u 1
3234.2.a.v 1
3234.2.a.w 2
3234.2.a.x 2
3234.2.a.y 2
3234.2.a.z 2
3234.2.a.ba 2
3234.2.a.bb 2
3234.2.a.bc 2
3234.2.a.bd 2
3234.2.a.be 2
3234.2.a.bf 3
3234.2.a.bg 3
3234.2.a.bh 3
3234.2.a.bi 3
3234.2.a.bj 4
3234.2.a.bk 4
3234.2.a.bl 4
3234.2.a.bm 4
3234.2.c $$\chi_{3234}(197, \cdot)$$ n/a 164 1
3234.2.e $$\chi_{3234}(2155, \cdot)$$ 3234.2.e.a 16 1
3234.2.e.b 16
3234.2.e.c 24
3234.2.e.d 24
3234.2.g $$\chi_{3234}(881, \cdot)$$ n/a 136 1
3234.2.i $$\chi_{3234}(67, \cdot)$$ n/a 136 2
3234.2.j $$\chi_{3234}(295, \cdot)$$ n/a 328 4
3234.2.k $$\chi_{3234}(815, \cdot)$$ n/a 264 2
3234.2.n $$\chi_{3234}(263, \cdot)$$ n/a 320 2
3234.2.p $$\chi_{3234}(901, \cdot)$$ n/a 160 2
3234.2.r $$\chi_{3234}(463, \cdot)$$ n/a 576 6
3234.2.t $$\chi_{3234}(587, \cdot)$$ n/a 640 4
3234.2.v $$\chi_{3234}(391, \cdot)$$ n/a 320 4
3234.2.x $$\chi_{3234}(491, \cdot)$$ n/a 656 4
3234.2.ba $$\chi_{3234}(419, \cdot)$$ n/a 1104 6
3234.2.bc $$\chi_{3234}(307, \cdot)$$ n/a 672 6
3234.2.be $$\chi_{3234}(659, \cdot)$$ n/a 1344 6
3234.2.bg $$\chi_{3234}(361, \cdot)$$ n/a 640 8
3234.2.bh $$\chi_{3234}(331, \cdot)$$ n/a 1104 12
3234.2.bj $$\chi_{3234}(19, \cdot)$$ n/a 640 8
3234.2.bl $$\chi_{3234}(557, \cdot)$$ n/a 1280 8
3234.2.bo $$\chi_{3234}(509, \cdot)$$ n/a 1280 8
3234.2.bp $$\chi_{3234}(169, \cdot)$$ n/a 2688 24
3234.2.br $$\chi_{3234}(241, \cdot)$$ n/a 1344 12
3234.2.bt $$\chi_{3234}(65, \cdot)$$ n/a 2688 12
3234.2.bw $$\chi_{3234}(89, \cdot)$$ n/a 2256 12
3234.2.by $$\chi_{3234}(29, \cdot)$$ n/a 5376 24
3234.2.ca $$\chi_{3234}(13, \cdot)$$ n/a 2688 24
3234.2.cc $$\chi_{3234}(125, \cdot)$$ n/a 5376 24
3234.2.ce $$\chi_{3234}(25, \cdot)$$ n/a 5376 48
3234.2.cf $$\chi_{3234}(5, \cdot)$$ n/a 10752 48
3234.2.ci $$\chi_{3234}(95, \cdot)$$ n/a 10752 48
3234.2.ck $$\chi_{3234}(61, \cdot)$$ n/a 5376 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(3234))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(3234)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(66))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(147))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(154))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(231))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(294))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(462))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(539))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1078))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1617))$$$$^{\oplus 2}$$