Properties

Label 8033.2
Level 8033
Weight 2
Dimension 2671589
Nonzero newspaces 48
Sturm bound 10741920

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Defining parameters

Level: \( N \) = \( 8033 = 29 \cdot 277 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(10741920\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8033))\).

Total New Old
Modular forms 2693208 2686441 6767
Cusp forms 2677753 2671589 6164
Eisenstein series 15455 14852 603

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8033))\)

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
8033.2.a \(\chi_{8033}(1, \cdot)\) 8033.2.a.a 1 1
8033.2.a.b 153
8033.2.a.c 154
8033.2.a.d 168
8033.2.a.e 169
8033.2.b \(\chi_{8033}(4987, \cdot)\) n/a 690 1
8033.2.c \(\chi_{8033}(3046, \cdot)\) n/a 650 1
8033.2.d \(\chi_{8033}(8032, \cdot)\) n/a 692 1
8033.2.e \(\chi_{8033}(2930, \cdot)\) n/a 1296 2
8033.2.f \(\chi_{8033}(771, \cdot)\) n/a 1386 2
8033.2.k \(\chi_{8033}(2830, \cdot)\) n/a 1386 2
8033.2.l \(\chi_{8033}(117, \cdot)\) n/a 1296 2
8033.2.m \(\chi_{8033}(2609, \cdot)\) n/a 1388 2
8033.2.n \(\chi_{8033}(2377, \cdot)\) n/a 1384 2
8033.2.o \(\chi_{8033}(832, \cdot)\) n/a 4140 6
8033.2.p \(\chi_{8033}(1143, \cdot)\) n/a 2772 4
8033.2.u \(\chi_{8033}(1844, \cdot)\) n/a 2772 4
8033.2.v \(\chi_{8033}(1107, \cdot)\) n/a 4152 6
8033.2.w \(\chi_{8033}(1938, \cdot)\) n/a 4164 6
8033.2.x \(\chi_{8033}(555, \cdot)\) n/a 4140 6
8033.2.y \(\chi_{8033}(393, \cdot)\) n/a 8304 12
8033.2.z \(\chi_{8033}(30, \cdot)\) n/a 14300 22
8033.2.ba \(\chi_{8033}(60, \cdot)\) n/a 8316 12
8033.2.bf \(\chi_{8033}(217, \cdot)\) n/a 8316 12
8033.2.bg \(\chi_{8033}(671, \cdot)\) n/a 8304 12
8033.2.bh \(\chi_{8033}(991, \cdot)\) n/a 8328 12
8033.2.bi \(\chi_{8033}(161, \cdot)\) n/a 8328 12
8033.2.bj \(\chi_{8033}(318, \cdot)\) n/a 15224 22
8033.2.bk \(\chi_{8033}(59, \cdot)\) n/a 14300 22
8033.2.bl \(\chi_{8033}(434, \cdot)\) n/a 15268 22
8033.2.bm \(\chi_{8033}(88, \cdot)\) n/a 28512 44
8033.2.bn \(\chi_{8033}(95, \cdot)\) n/a 16632 24
8033.2.bs \(\chi_{8033}(182, \cdot)\) n/a 16632 24
8033.2.bt \(\chi_{8033}(104, \cdot)\) n/a 30492 44
8033.2.by \(\chi_{8033}(331, \cdot)\) n/a 30492 44
8033.2.bz \(\chi_{8033}(86, \cdot)\) n/a 30448 44
8033.2.ca \(\chi_{8033}(28, \cdot)\) n/a 30536 44
8033.2.cb \(\chi_{8033}(407, \cdot)\) n/a 28512 44
8033.2.cc \(\chi_{8033}(16, \cdot)\) n/a 91344 132
8033.2.cd \(\chi_{8033}(17, \cdot)\) n/a 60984 88
8033.2.ci \(\chi_{8033}(99, \cdot)\) n/a 60984 88
8033.2.cj \(\chi_{8033}(236, \cdot)\) n/a 91608 132
8033.2.ck \(\chi_{8033}(74, \cdot)\) n/a 91608 132
8033.2.cl \(\chi_{8033}(4, \cdot)\) n/a 91344 132
8033.2.cm \(\chi_{8033}(23, \cdot)\) n/a 182688 264
8033.2.cn \(\chi_{8033}(37, \cdot)\) n/a 182952 264
8033.2.cs \(\chi_{8033}(2, \cdot)\) n/a 182952 264
8033.2.ct \(\chi_{8033}(7, \cdot)\) n/a 183216 264
8033.2.cu \(\chi_{8033}(9, \cdot)\) n/a 183216 264
8033.2.cv \(\chi_{8033}(22, \cdot)\) n/a 182688 264
8033.2.cw \(\chi_{8033}(14, \cdot)\) n/a 365904 528
8033.2.db \(\chi_{8033}(11, \cdot)\) n/a 365904 528

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8033))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8033)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(277))\)\(^{\oplus 2}\)