# Properties

 Label 9216.2 Level 9216 Weight 2 Dimension 1048464 Nonzero newspaces 32 Sturm bound 9437184

## Defining parameters

 Level: $$N$$ = $$9216 = 2^{10} \cdot 3^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$32$$ Sturm bound: $$9437184$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(9216))$$.

Total New Old
Modular forms 2372608 1052784 1319824
Cusp forms 2345985 1048464 1297521
Eisenstein series 26623 4320 22303

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(9216))$$

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
9216.2.a $$\chi_{9216}(1, \cdot)$$ 9216.2.a.a 2 1
9216.2.a.b 2
9216.2.a.c 2
9216.2.a.d 2
9216.2.a.e 2
9216.2.a.f 2
9216.2.a.g 2
9216.2.a.h 2
9216.2.a.i 2
9216.2.a.j 2
9216.2.a.k 2
9216.2.a.l 2
9216.2.a.m 2
9216.2.a.n 2
9216.2.a.o 2
9216.2.a.p 2
9216.2.a.q 2
9216.2.a.r 2
9216.2.a.s 2
9216.2.a.t 2
9216.2.a.u 2
9216.2.a.v 2
9216.2.a.w 4
9216.2.a.x 4
9216.2.a.y 4
9216.2.a.z 4
9216.2.a.ba 4
9216.2.a.bb 4
9216.2.a.bc 4
9216.2.a.bd 4
9216.2.a.be 4
9216.2.a.bf 4
9216.2.a.bg 4
9216.2.a.bh 4
9216.2.a.bi 4
9216.2.a.bj 4
9216.2.a.bk 4
9216.2.a.bl 4
9216.2.a.bm 4
9216.2.a.bn 4
9216.2.a.bo 4
9216.2.a.bp 4
9216.2.a.bq 8
9216.2.a.br 8
9216.2.a.bs 8
9216.2.a.bt 8
9216.2.c $$\chi_{9216}(9215, \cdot)$$ n/a 128 1
9216.2.d $$\chi_{9216}(4609, \cdot)$$ n/a 156 1
9216.2.f $$\chi_{9216}(4607, \cdot)$$ n/a 128 1
9216.2.i $$\chi_{9216}(3073, \cdot)$$ n/a 752 2
9216.2.k $$\chi_{9216}(2305, \cdot)$$ n/a 312 2
9216.2.l $$\chi_{9216}(2303, \cdot)$$ n/a 256 2
9216.2.p $$\chi_{9216}(1535, \cdot)$$ n/a 752 2
9216.2.r $$\chi_{9216}(1537, \cdot)$$ n/a 752 2
9216.2.s $$\chi_{9216}(3071, \cdot)$$ n/a 752 2
9216.2.v $$\chi_{9216}(1153, \cdot)$$ n/a 640 4
9216.2.w $$\chi_{9216}(1151, \cdot)$$ n/a 512 4
9216.2.y $$\chi_{9216}(767, \cdot)$$ n/a 1504 4
9216.2.bb $$\chi_{9216}(769, \cdot)$$ n/a 1504 4
9216.2.bd $$\chi_{9216}(577, \cdot)$$ n/a 1248 8
9216.2.be $$\chi_{9216}(575, \cdot)$$ n/a 1024 8
9216.2.bg $$\chi_{9216}(385, \cdot)$$ n/a 3072 8
9216.2.bj $$\chi_{9216}(383, \cdot)$$ n/a 3072 8
9216.2.bl $$\chi_{9216}(289, \cdot)$$ n/a 2528 16
9216.2.bm $$\chi_{9216}(287, \cdot)$$ n/a 2048 16
9216.2.bp $$\chi_{9216}(191, \cdot)$$ n/a 6016 16
9216.2.bq $$\chi_{9216}(193, \cdot)$$ n/a 6016 16
9216.2.bt $$\chi_{9216}(145, \cdot)$$ n/a 5088 32
9216.2.bu $$\chi_{9216}(143, \cdot)$$ n/a 4096 32
9216.2.bw $$\chi_{9216}(95, \cdot)$$ n/a 12160 32
9216.2.bz $$\chi_{9216}(97, \cdot)$$ n/a 12160 32
9216.2.cb $$\chi_{9216}(73, \cdot)$$ None 0 64
9216.2.cc $$\chi_{9216}(71, \cdot)$$ None 0 64
9216.2.ce $$\chi_{9216}(49, \cdot)$$ n/a 24448 64
9216.2.ch $$\chi_{9216}(47, \cdot)$$ n/a 24448 64
9216.2.cj $$\chi_{9216}(37, \cdot)$$ n/a 81792 128
9216.2.ck $$\chi_{9216}(35, \cdot)$$ n/a 65536 128
9216.2.cn $$\chi_{9216}(23, \cdot)$$ None 0 128
9216.2.co $$\chi_{9216}(25, \cdot)$$ None 0 128
9216.2.cq $$\chi_{9216}(11, \cdot)$$ n/a 392704 256
9216.2.ct $$\chi_{9216}(13, \cdot)$$ n/a 392704 256

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(9216))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(9216)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 21}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 15}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(96))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(128))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(144))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(192))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(256))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(288))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(384))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(512))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(576))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(768))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1024))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1152))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1536))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2304))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3072))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4608))$$$$^{\oplus 2}$$