Properties

Label 8024.2
Level 8024
Weight 2
Dimension 1115626
Nonzero newspaces 30
Sturm bound 8017920

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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

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