# Properties

 Label 8024.2 Level 8024 Weight 2 Dimension 1.11563e+06 Nonzero newspaces 30 Sturm bound 8.01792e+06

## Defining parameters

 Level: $$N$$ = $$8024 = 2^{3} \cdot 17 \cdot 59$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$30$$ Sturm bound: $$8017920$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8024))$$.

Total New Old
Modular forms 2015616 1122466 893150
Cusp forms 1993345 1115626 877719
Eisenstein series 22271 6840 15431

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8024))$$

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
8024.2.a $$\chi_{8024}(1, \cdot)$$ 8024.2.a.a 1 1
8024.2.a.b 1
8024.2.a.c 1
8024.2.a.d 1
8024.2.a.e 1
8024.2.a.f 1
8024.2.a.g 1
8024.2.a.h 1
8024.2.a.i 1
8024.2.a.j 1
8024.2.a.k 1
8024.2.a.l 1
8024.2.a.m 1
8024.2.a.n 1
8024.2.a.o 1
8024.2.a.p 2
8024.2.a.q 2
8024.2.a.r 2
8024.2.a.s 3
8024.2.a.t 3
8024.2.a.u 3
8024.2.a.v 18
8024.2.a.w 20
8024.2.a.x 22
8024.2.a.y 23
8024.2.a.z 24
8024.2.a.ba 30
8024.2.a.bb 32
8024.2.a.bc 33
8024.2.b $$\chi_{8024}(4249, \cdot)$$ n/a 262 1
8024.2.d $$\chi_{8024}(4013, \cdot)$$ n/a 928 1
8024.2.g $$\chi_{8024}(3775, \cdot)$$ None 0 1
8024.2.i $$\chi_{8024}(4011, \cdot)$$ n/a 1076 1
8024.2.j $$\chi_{8024}(7787, \cdot)$$ n/a 960 1
8024.2.l $$\chi_{8024}(8023, \cdot)$$ None 0 1
8024.2.o $$\chi_{8024}(237, \cdot)$$ n/a 1044 1
8024.2.r $$\chi_{8024}(1653, \cdot)$$ n/a 2088 2
8024.2.t $$\chi_{8024}(1415, \cdot)$$ None 0 2
8024.2.u $$\chi_{8024}(5665, \cdot)$$ n/a 524 2
8024.2.w $$\chi_{8024}(5427, \cdot)$$ n/a 2152 2
8024.2.z $$\chi_{8024}(1889, \cdot)$$ n/a 1040 4
8024.2.bb $$\chi_{8024}(1651, \cdot)$$ n/a 4304 4
8024.2.bc $$\chi_{8024}(943, \cdot)$$ None 0 4
8024.2.be $$\chi_{8024}(1181, \cdot)$$ n/a 4176 4
8024.2.bh $$\chi_{8024}(1535, \cdot)$$ None 0 8
8024.2.bi $$\chi_{8024}(827, \cdot)$$ n/a 8352 8
8024.2.bl $$\chi_{8024}(589, \cdot)$$ n/a 8608 8
8024.2.bm $$\chi_{8024}(1297, \cdot)$$ n/a 2160 8
8024.2.bo $$\chi_{8024}(137, \cdot)$$ n/a 6720 28
8024.2.bq $$\chi_{8024}(373, \cdot)$$ n/a 30128 28
8024.2.bt $$\chi_{8024}(679, \cdot)$$ None 0 28
8024.2.bv $$\chi_{8024}(443, \cdot)$$ n/a 26880 28
8024.2.bw $$\chi_{8024}(67, \cdot)$$ n/a 30128 28
8024.2.by $$\chi_{8024}(103, \cdot)$$ None 0 28
8024.2.cb $$\chi_{8024}(205, \cdot)$$ n/a 26880 28
8024.2.cd $$\chi_{8024}(169, \cdot)$$ n/a 7560 28
8024.2.cf $$\chi_{8024}(115, \cdot)$$ n/a 60256 56
8024.2.ch $$\chi_{8024}(81, \cdot)$$ n/a 15120 56
8024.2.ci $$\chi_{8024}(47, \cdot)$$ None 0 56
8024.2.ck $$\chi_{8024}(21, \cdot)$$ n/a 60256 56
8024.2.cn $$\chi_{8024}(53, \cdot)$$ n/a 120512 112
8024.2.cp $$\chi_{8024}(111, \cdot)$$ None 0 112
8024.2.cq $$\chi_{8024}(43, \cdot)$$ n/a 120512 112
8024.2.cs $$\chi_{8024}(9, \cdot)$$ n/a 30240 112
8024.2.cv $$\chi_{8024}(65, \cdot)$$ n/a 60480 224
8024.2.cw $$\chi_{8024}(37, \cdot)$$ n/a 241024 224
8024.2.cz $$\chi_{8024}(3, \cdot)$$ n/a 241024 224
8024.2.da $$\chi_{8024}(7, \cdot)$$ None 0 224

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8024))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8024)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(34))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(59))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(68))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(118))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(136))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(236))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(472))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1003))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2006))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4012))$$$$^{\oplus 2}$$