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Properties

Label 4248.2
Level 4248
Weight 2
Dimension 222001
Nonzero newspaces 24
Sturm bound 2004480

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Defining parameters

Level: \( N \) = \( 4248 = 2^{3} \cdot 3^{2} \cdot 59 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(2004480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4248))\).

Total New Old
Modular forms 506688 224053 282635
Cusp forms 495553 222001 273552
Eisenstein series 11135 2052 9083

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4248))\)

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
4248.2.a \(\chi_{4248}(1, \cdot)\) 4248.2.a.a 1 1
4248.2.a.b 1
4248.2.a.c 1
4248.2.a.d 1
4248.2.a.e 1
4248.2.a.f 1
4248.2.a.g 1
4248.2.a.h 1
4248.2.a.i 1
4248.2.a.j 2
4248.2.a.k 2
4248.2.a.l 3
4248.2.a.m 3
4248.2.a.n 3
4248.2.a.o 4
4248.2.a.p 4
4248.2.a.q 5
4248.2.a.r 5
4248.2.a.s 5
4248.2.a.t 6
4248.2.a.u 6
4248.2.a.v 8
4248.2.a.w 8
4248.2.c \(\chi_{4248}(235, \cdot)\) n/a 298 1
4248.2.e \(\chi_{4248}(2951, \cdot)\) None 0 1
4248.2.f \(\chi_{4248}(2125, \cdot)\) n/a 290 1
4248.2.h \(\chi_{4248}(3185, \cdot)\) 4248.2.h.a 2 1
4248.2.h.b 2
4248.2.h.c 28
4248.2.h.d 28
4248.2.j \(\chi_{4248}(827, \cdot)\) n/a 232 1
4248.2.l \(\chi_{4248}(2359, \cdot)\) None 0 1
4248.2.o \(\chi_{4248}(1061, \cdot)\) n/a 240 1
4248.2.q \(\chi_{4248}(1417, \cdot)\) n/a 348 2
4248.2.s \(\chi_{4248}(2477, \cdot)\) n/a 1432 2
4248.2.v \(\chi_{4248}(943, \cdot)\) None 0 2
4248.2.x \(\chi_{4248}(2243, \cdot)\) n/a 1392 2
4248.2.z \(\chi_{4248}(353, \cdot)\) n/a 360 2
4248.2.bb \(\chi_{4248}(709, \cdot)\) n/a 1392 2
4248.2.bc \(\chi_{4248}(119, \cdot)\) None 0 2
4248.2.be \(\chi_{4248}(1651, \cdot)\) n/a 1432 2
4248.2.bg \(\chi_{4248}(145, \cdot)\) n/a 2100 28
4248.2.bi \(\chi_{4248}(269, \cdot)\) n/a 6720 28
4248.2.bl \(\chi_{4248}(55, \cdot)\) None 0 28
4248.2.bn \(\chi_{4248}(35, \cdot)\) n/a 6720 28
4248.2.bp \(\chi_{4248}(89, \cdot)\) n/a 1680 28
4248.2.br \(\chi_{4248}(181, \cdot)\) n/a 8344 28
4248.2.bs \(\chi_{4248}(71, \cdot)\) None 0 28
4248.2.bu \(\chi_{4248}(91, \cdot)\) n/a 8344 28
4248.2.bw \(\chi_{4248}(25, \cdot)\) n/a 10080 56
4248.2.by \(\chi_{4248}(43, \cdot)\) n/a 40096 56
4248.2.ca \(\chi_{4248}(95, \cdot)\) None 0 56
4248.2.cb \(\chi_{4248}(85, \cdot)\) n/a 40096 56
4248.2.cd \(\chi_{4248}(65, \cdot)\) n/a 10080 56
4248.2.cf \(\chi_{4248}(203, \cdot)\) n/a 40096 56
4248.2.ch \(\chi_{4248}(31, \cdot)\) None 0 56
4248.2.ck \(\chi_{4248}(77, \cdot)\) n/a 40096 56

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4248))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4248)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(118))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(177))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(236))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(354))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(472))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(531))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(708))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1062))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1416))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2124))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4248))\)\(^{\oplus 1}\)