Properties

Label 8003.2
Level 8003
Weight 2
Dimension 2657865
Nonzero newspaces 36
Sturm bound 10670400

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Defining parameters

Level: \( N \) = \( 8003 = 53 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(10670400\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8003))\).

Total New Old
Modular forms 2675400 2673065 2335
Cusp forms 2659801 2657865 1936
Eisenstein series 15599 15200 399

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8003))\)

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
8003.2.a \(\chi_{8003}(1, \cdot)\) 8003.2.a.a 147 1
8003.2.a.b 153
8003.2.a.c 172
8003.2.a.d 179
8003.2.b \(\chi_{8003}(6041, \cdot)\) n/a 674 1
8003.2.e \(\chi_{8003}(1326, \cdot)\) n/a 1316 2
8003.2.g \(\chi_{8003}(2415, \cdot)\) n/a 1364 2
8003.2.h \(\chi_{8003}(5142, \cdot)\) n/a 2640 4
8003.2.j \(\chi_{8003}(3656, \cdot)\) n/a 1364 2
8003.2.m \(\chi_{8003}(3179, \cdot)\) n/a 2728 4
8003.2.o \(\chi_{8003}(1090, \cdot)\) n/a 2728 4
8003.2.q \(\chi_{8003}(152, \cdot)\) n/a 8112 12
8003.2.r \(\chi_{8003}(1061, \cdot)\) n/a 5264 8
8003.2.s \(\chi_{8003}(394, \cdot)\) n/a 5456 8
8003.2.u \(\chi_{8003}(160, \cdot)\) n/a 13200 20
8003.2.x \(\chi_{8003}(303, \cdot)\) n/a 8088 12
8003.2.ba \(\chi_{8003}(105, \cdot)\) n/a 5456 8
8003.2.bb \(\chi_{8003}(183, \cdot)\) n/a 16368 24
8003.2.be \(\chi_{8003}(370, \cdot)\) n/a 13640 20
8003.2.bf \(\chi_{8003}(603, \cdot)\) n/a 16368 24
8003.2.bi \(\chi_{8003}(23, \cdot)\) n/a 10912 16
8003.2.bj \(\chi_{8003}(819, \cdot)\) n/a 32736 48
8003.2.bk \(\chi_{8003}(213, \cdot)\) n/a 26320 40
8003.2.bm \(\chi_{8003}(269, \cdot)\) n/a 16368 24
8003.2.bp \(\chi_{8003}(83, \cdot)\) n/a 27280 40
8003.2.br \(\chi_{8003}(59, \cdot)\) n/a 32736 48
8003.2.bt \(\chi_{8003}(423, \cdot)\) n/a 27280 40
8003.2.bx \(\chi_{8003}(33, \cdot)\) n/a 32736 48
8003.2.by \(\chi_{8003}(16, \cdot)\) n/a 65472 96
8003.2.ca \(\chi_{8003}(87, \cdot)\) n/a 65472 96
8003.2.cb \(\chi_{8003}(30, \cdot)\) n/a 54560 80
8003.2.cd \(\chi_{8003}(44, \cdot)\) n/a 163680 240
8003.2.ce \(\chi_{8003}(4, \cdot)\) n/a 65472 96
8003.2.ci \(\chi_{8003}(9, \cdot)\) n/a 163680 240
8003.2.ck \(\chi_{8003}(75, \cdot)\) n/a 130944 192
8003.2.cm \(\chi_{8003}(10, \cdot)\) n/a 327360 480
8003.2.cn \(\chi_{8003}(3, \cdot)\) n/a 327360 480
8003.2.cq \(\chi_{8003}(11, \cdot)\) n/a 327360 480
8003.2.ct \(\chi_{8003}(12, \cdot)\) n/a 654720 960

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8003))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8003)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(53))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(151))\)\(^{\oplus 2}\)