# Properties

 Label 9196.2 Level 9196 Weight 2 Dimension 1486397 Nonzero newspaces 48 Sturm bound 10454400

## Defining parameters

 Level: $$N$$ = $$9196 = 2^{2} \cdot 11^{2} \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$10454400$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(9196))$$.

Total New Old
Modular forms 2628000 1495953 1132047
Cusp forms 2599201 1486397 1112804
Eisenstein series 28799 9556 19243

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(9196))$$

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
9196.2.a $$\chi_{9196}(1, \cdot)$$ 9196.2.a.a 1 1
9196.2.a.b 1
9196.2.a.c 1
9196.2.a.d 1
9196.2.a.e 1
9196.2.a.f 1
9196.2.a.g 1
9196.2.a.h 2
9196.2.a.i 6
9196.2.a.j 6
9196.2.a.k 6
9196.2.a.l 6
9196.2.a.m 6
9196.2.a.n 6
9196.2.a.o 7
9196.2.a.p 7
9196.2.a.q 8
9196.2.a.r 8
9196.2.a.s 10
9196.2.a.t 10
9196.2.a.u 14
9196.2.a.v 14
9196.2.a.w 20
9196.2.a.x 20
9196.2.b $$\chi_{9196}(4597, \cdot)$$ n/a 180 1
9196.2.d $$\chi_{9196}(7259, \cdot)$$ n/a 972 1
9196.2.g $$\chi_{9196}(6535, \cdot)$$ n/a 1072 1
9196.2.i $$\chi_{9196}(3389, \cdot)$$ n/a 362 2
9196.2.j $$\chi_{9196}(2205, \cdot)$$ n/a 648 4
9196.2.k $$\chi_{9196}(3147, \cdot)$$ n/a 2144 2
9196.2.o $$\chi_{9196}(1209, \cdot)$$ n/a 360 2
9196.2.q $$\chi_{9196}(1451, \cdot)$$ n/a 2128 2
9196.2.r $$\chi_{9196}(1453, \cdot)$$ n/a 1092 6
9196.2.t $$\chi_{9196}(1291, \cdot)$$ n/a 4256 4
9196.2.w $$\chi_{9196}(723, \cdot)$$ n/a 3888 4
9196.2.y $$\chi_{9196}(645, \cdot)$$ n/a 720 4
9196.2.z $$\chi_{9196}(837, \cdot)$$ n/a 1980 10
9196.2.ba $$\chi_{9196}(729, \cdot)$$ n/a 1440 8
9196.2.bd $$\chi_{9196}(967, \cdot)$$ n/a 6384 6
9196.2.be $$\chi_{9196}(243, \cdot)$$ n/a 6432 6
9196.2.bg $$\chi_{9196}(241, \cdot)$$ n/a 1080 6
9196.2.bj $$\chi_{9196}(571, \cdot)$$ n/a 11880 10
9196.2.bl $$\chi_{9196}(417, \cdot)$$ n/a 2200 10
9196.2.bn $$\chi_{9196}(683, \cdot)$$ n/a 13160 10
9196.2.bp $$\chi_{9196}(239, \cdot)$$ n/a 8512 8
9196.2.br $$\chi_{9196}(1129, \cdot)$$ n/a 1440 8
9196.2.bv $$\chi_{9196}(27, \cdot)$$ n/a 8512 8
9196.2.bw $$\chi_{9196}(45, \cdot)$$ n/a 4400 20
9196.2.bx $$\chi_{9196}(9, \cdot)$$ n/a 4320 24
9196.2.by $$\chi_{9196}(229, \cdot)$$ n/a 7920 40
9196.2.cb $$\chi_{9196}(331, \cdot)$$ n/a 26320 20
9196.2.cc $$\chi_{9196}(87, \cdot)$$ n/a 26320 20
9196.2.ce $$\chi_{9196}(65, \cdot)$$ n/a 4400 20
9196.2.ch $$\chi_{9196}(717, \cdot)$$ n/a 4320 24
9196.2.cj $$\chi_{9196}(3, \cdot)$$ n/a 25536 24
9196.2.ck $$\chi_{9196}(215, \cdot)$$ n/a 25536 24
9196.2.cn $$\chi_{9196}(177, \cdot)$$ n/a 13200 60
9196.2.cp $$\chi_{9196}(75, \cdot)$$ n/a 52640 40
9196.2.cr $$\chi_{9196}(189, \cdot)$$ n/a 8800 40
9196.2.ct $$\chi_{9196}(39, \cdot)$$ n/a 47520 40
9196.2.cv $$\chi_{9196}(49, \cdot)$$ n/a 17600 80
9196.2.cx $$\chi_{9196}(67, \cdot)$$ n/a 78960 60
9196.2.cz $$\chi_{9196}(21, \cdot)$$ n/a 13200 60
9196.2.db $$\chi_{9196}(43, \cdot)$$ n/a 78960 60
9196.2.de $$\chi_{9196}(145, \cdot)$$ n/a 17600 80
9196.2.dg $$\chi_{9196}(7, \cdot)$$ n/a 105280 80
9196.2.dh $$\chi_{9196}(31, \cdot)$$ n/a 105280 80
9196.2.dk $$\chi_{9196}(5, \cdot)$$ n/a 52800 240
9196.2.dm $$\chi_{9196}(35, \cdot)$$ n/a 315840 240
9196.2.do $$\chi_{9196}(13, \cdot)$$ n/a 52800 240
9196.2.dq $$\chi_{9196}(15, \cdot)$$ n/a 315840 240

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(9196))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(9196)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(121))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(209))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(242))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(418))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(484))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(836))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2299))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4598))$$$$^{\oplus 2}$$