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Properties

Label 4416.2
Level 4416
Weight 2
Dimension 226308
Nonzero newspaces 32
Sturm bound 2162688

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Defining parameters

Level: \( N \) = \( 4416 = 2^{6} \cdot 3 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(2162688\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4416))\).

Total New Old
Modular forms 547008 228156 318852
Cusp forms 534337 226308 308029
Eisenstein series 12671 1848 10823

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4416))\)

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
4416.2.a \(\chi_{4416}(1, \cdot)\) 4416.2.a.a 1 1
4416.2.a.b 1
4416.2.a.c 1
4416.2.a.d 1
4416.2.a.e 1
4416.2.a.f 1
4416.2.a.g 1
4416.2.a.h 1
4416.2.a.i 1
4416.2.a.j 1
4416.2.a.k 1
4416.2.a.l 1
4416.2.a.m 1
4416.2.a.n 1
4416.2.a.o 1
4416.2.a.p 1
4416.2.a.q 1
4416.2.a.r 1
4416.2.a.s 1
4416.2.a.t 1
4416.2.a.u 1
4416.2.a.v 1
4416.2.a.w 1
4416.2.a.x 1
4416.2.a.y 1
4416.2.a.z 1
4416.2.a.ba 1
4416.2.a.bb 1
4416.2.a.bc 2
4416.2.a.bd 2
4416.2.a.be 2
4416.2.a.bf 2
4416.2.a.bg 2
4416.2.a.bh 2
4416.2.a.bi 2
4416.2.a.bj 2
4416.2.a.bk 2
4416.2.a.bl 2
4416.2.a.bm 2
4416.2.a.bn 2
4416.2.a.bo 3
4416.2.a.bp 3
4416.2.a.bq 3
4416.2.a.br 3
4416.2.a.bs 3
4416.2.a.bt 3
4416.2.a.bu 4
4416.2.a.bv 4
4416.2.a.bw 5
4416.2.a.bx 5
4416.2.b \(\chi_{4416}(4001, \cdot)\) n/a 192 1
4416.2.e \(\chi_{4416}(1151, \cdot)\) n/a 176 1
4416.2.f \(\chi_{4416}(2209, \cdot)\) 4416.2.f.a 4 1
4416.2.f.b 4
4416.2.f.c 8
4416.2.f.d 8
4416.2.f.e 8
4416.2.f.f 8
4416.2.f.g 8
4416.2.f.h 8
4416.2.f.i 16
4416.2.f.j 16
4416.2.i \(\chi_{4416}(1471, \cdot)\) 4416.2.i.a 8 1
4416.2.i.b 16
4416.2.i.c 24
4416.2.i.d 24
4416.2.i.e 24
4416.2.j \(\chi_{4416}(3359, \cdot)\) n/a 176 1
4416.2.m \(\chi_{4416}(1793, \cdot)\) n/a 188 1
4416.2.n \(\chi_{4416}(3679, \cdot)\) 4416.2.n.a 8 1
4416.2.n.b 8
4416.2.n.c 8
4416.2.n.d 8
4416.2.n.e 32
4416.2.n.f 32
4416.2.q \(\chi_{4416}(367, \cdot)\) n/a 192 2
4416.2.t \(\chi_{4416}(1105, \cdot)\) n/a 176 2
4416.2.u \(\chi_{4416}(47, \cdot)\) n/a 352 2
4416.2.x \(\chi_{4416}(689, \cdot)\) n/a 376 2
4416.2.ba \(\chi_{4416}(553, \cdot)\) None 0 4
4416.2.bb \(\chi_{4416}(137, \cdot)\) None 0 4
4416.2.bc \(\chi_{4416}(599, \cdot)\) None 0 4
4416.2.bd \(\chi_{4416}(919, \cdot)\) None 0 4
4416.2.bg \(\chi_{4416}(193, \cdot)\) n/a 960 10
4416.2.bj \(\chi_{4416}(277, \cdot)\) n/a 2816 8
4416.2.bk \(\chi_{4416}(413, \cdot)\) n/a 6112 8
4416.2.bl \(\chi_{4416}(323, \cdot)\) n/a 5632 8
4416.2.bm \(\chi_{4416}(91, \cdot)\) n/a 3072 8
4416.2.br \(\chi_{4416}(799, \cdot)\) n/a 960 10
4416.2.bs \(\chi_{4416}(65, \cdot)\) n/a 1880 10
4416.2.bv \(\chi_{4416}(95, \cdot)\) n/a 1920 10
4416.2.bw \(\chi_{4416}(319, \cdot)\) n/a 960 10
4416.2.bz \(\chi_{4416}(289, \cdot)\) n/a 960 10
4416.2.ca \(\chi_{4416}(767, \cdot)\) n/a 1880 10
4416.2.cd \(\chi_{4416}(1121, \cdot)\) n/a 1920 10
4416.2.ce \(\chi_{4416}(17, \cdot)\) n/a 3760 20
4416.2.ch \(\chi_{4416}(239, \cdot)\) n/a 3760 20
4416.2.ci \(\chi_{4416}(49, \cdot)\) n/a 1920 20
4416.2.cl \(\chi_{4416}(79, \cdot)\) n/a 1920 20
4416.2.co \(\chi_{4416}(71, \cdot)\) None 0 40
4416.2.cp \(\chi_{4416}(7, \cdot)\) None 0 40
4416.2.cq \(\chi_{4416}(25, \cdot)\) None 0 40
4416.2.cr \(\chi_{4416}(89, \cdot)\) None 0 40
4416.2.cw \(\chi_{4416}(19, \cdot)\) n/a 30720 80
4416.2.cx \(\chi_{4416}(35, \cdot)\) n/a 61120 80
4416.2.cy \(\chi_{4416}(5, \cdot)\) n/a 61120 80
4416.2.cz \(\chi_{4416}(13, \cdot)\) n/a 30720 80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4416))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4416)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(276))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(368))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(552))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(736))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1104))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1472))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2208))\)\(^{\oplus 2}\)