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Properties

Label 9583.2
Level 9583
Weight 2
Dimension 3574735
Nonzero newspaces 48
Sturm bound 14982336

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Defining parameters

Level: \( N \) = \( 9583 = 7 \cdot 37^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(14982336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9583))\).

Total New Old
Modular forms 3757464 3593819 163645
Cusp forms 3733705 3574735 158970
Eisenstein series 23759 19084 4675

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9583))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
9583.2.a \(\chi_{9583}(1, \cdot)\) 9583.2.a.a 1 1
9583.2.a.b 1
9583.2.a.c 1
9583.2.a.d 2
9583.2.a.e 2
9583.2.a.f 2
9583.2.a.g 3
9583.2.a.h 3
9583.2.a.i 4
9583.2.a.j 4
9583.2.a.k 8
9583.2.a.l 8
9583.2.a.m 9
9583.2.a.n 9
9583.2.a.o 11
9583.2.a.p 11
9583.2.a.q 16
9583.2.a.r 18
9583.2.a.s 27
9583.2.a.t 27
9583.2.a.u 33
9583.2.a.v 33
9583.2.a.w 48
9583.2.a.x 60
9583.2.a.y 81
9583.2.a.z 81
9583.2.a.ba 81
9583.2.a.bb 81
9583.2.c \(\chi_{9583}(5475, \cdot)\) n/a 666 1
9583.2.e \(\chi_{9583}(2739, \cdot)\) n/a 1704 2
9583.2.f \(\chi_{9583}(3319, \cdot)\) n/a 1328 2
9583.2.g \(\chi_{9583}(1950, \cdot)\) n/a 1704 2
9583.2.h \(\chi_{9583}(3525, \cdot)\) n/a 1704 2
9583.2.j \(\chi_{9583}(1252, \cdot)\) n/a 1708 2
9583.2.l \(\chi_{9583}(4895, \cdot)\) n/a 1704 2
9583.2.p \(\chi_{9583}(788, \cdot)\) n/a 1704 2
9583.2.q \(\chi_{9583}(4106, \cdot)\) n/a 1704 2
9583.2.r \(\chi_{9583}(582, \cdot)\) n/a 1332 2
9583.2.w \(\chi_{9583}(932, \cdot)\) n/a 3984 6
9583.2.x \(\chi_{9583}(737, \cdot)\) n/a 5118 6
9583.2.y \(\chi_{9583}(1045, \cdot)\) n/a 5118 6
9583.2.ba \(\chi_{9583}(356, \cdot)\) n/a 3416 4
9583.2.bb \(\chi_{9583}(1013, \cdot)\) n/a 3408 4
9583.2.bc \(\chi_{9583}(117, \cdot)\) n/a 3408 4
9583.2.bg \(\chi_{9583}(1725, \cdot)\) n/a 3408 4
9583.2.bk \(\chi_{9583}(1723, \cdot)\) n/a 3996 6
9583.2.bl \(\chi_{9583}(354, \cdot)\) n/a 5118 6
9583.2.bm \(\chi_{9583}(324, \cdot)\) n/a 5118 6
9583.2.bq \(\chi_{9583}(348, \cdot)\) n/a 10236 12
9583.2.bt \(\chi_{9583}(1445, \cdot)\) n/a 10236 12
9583.2.bu \(\chi_{9583}(76, \cdot)\) n/a 10224 12
9583.2.bw \(\chi_{9583}(260, \cdot)\) n/a 25344 36
9583.2.by \(\chi_{9583}(36, \cdot)\) n/a 25272 36
9583.2.ca \(\chi_{9583}(100, \cdot)\) n/a 67392 72
9583.2.cb \(\chi_{9583}(121, \cdot)\) n/a 67392 72
9583.2.cc \(\chi_{9583}(211, \cdot)\) n/a 50688 72
9583.2.cd \(\chi_{9583}(149, \cdot)\) n/a 67392 72
9583.2.ce \(\chi_{9583}(6, \cdot)\) n/a 67248 72
9583.2.ck \(\chi_{9583}(64, \cdot)\) n/a 50544 72
9583.2.cl \(\chi_{9583}(184, \cdot)\) n/a 67392 72
9583.2.cm \(\chi_{9583}(11, \cdot)\) n/a 67392 72
9583.2.cq \(\chi_{9583}(233, \cdot)\) n/a 67392 72
9583.2.cs \(\chi_{9583}(9, \cdot)\) n/a 201960 216
9583.2.ct \(\chi_{9583}(44, \cdot)\) n/a 201960 216
9583.2.cu \(\chi_{9583}(71, \cdot)\) n/a 152064 216
9583.2.cv \(\chi_{9583}(82, \cdot)\) n/a 134784 144
9583.2.cz \(\chi_{9583}(31, \cdot)\) n/a 134784 144
9583.2.da \(\chi_{9583}(45, \cdot)\) n/a 134784 144
9583.2.db \(\chi_{9583}(97, \cdot)\) n/a 134496 144
9583.2.dg \(\chi_{9583}(4, \cdot)\) n/a 201960 216
9583.2.dh \(\chi_{9583}(25, \cdot)\) n/a 201960 216
9583.2.di \(\chi_{9583}(78, \cdot)\) n/a 151632 216
9583.2.dn \(\chi_{9583}(13, \cdot)\) n/a 404352 432
9583.2.do \(\chi_{9583}(5, \cdot)\) n/a 403920 432
9583.2.dr \(\chi_{9583}(24, \cdot)\) n/a 403920 432

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9583))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9583)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(259))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1369))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9583))\)\(^{\oplus 1}\)