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Properties

Label 7744.2
Level 7744
Weight 2
Dimension 1025141
Nonzero newspaces 32
Sturm bound 7434240

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Defining parameters

Level: \( N \) = \( 7744 = 2^{6} \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(7434240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7744))\).

Total New Old
Modular forms 1870080 1031323 838757
Cusp forms 1847041 1025141 821900
Eisenstein series 23039 6182 16857

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7744))\)

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
7744.2.a \(\chi_{7744}(1, \cdot)\) 7744.2.a.a 1 1
7744.2.a.b 1
7744.2.a.c 1
7744.2.a.d 1
7744.2.a.e 1
7744.2.a.f 1
7744.2.a.g 1
7744.2.a.h 1
7744.2.a.i 1
7744.2.a.j 1
7744.2.a.k 1
7744.2.a.l 1
7744.2.a.m 1
7744.2.a.n 1
7744.2.a.o 1
7744.2.a.p 1
7744.2.a.q 1
7744.2.a.r 1
7744.2.a.s 1
7744.2.a.t 1
7744.2.a.u 1
7744.2.a.v 1
7744.2.a.w 1
7744.2.a.x 1
7744.2.a.y 1
7744.2.a.z 1
7744.2.a.ba 1
7744.2.a.bb 1
7744.2.a.bc 1
7744.2.a.bd 1
7744.2.a.be 1
7744.2.a.bf 1
7744.2.a.bg 1
7744.2.a.bh 1
7744.2.a.bi 1
7744.2.a.bj 1
7744.2.a.bk 1
7744.2.a.bl 2
7744.2.a.bm 2
7744.2.a.bn 2
7744.2.a.bo 2
7744.2.a.bp 2
7744.2.a.bq 2
7744.2.a.br 2
7744.2.a.bs 2
7744.2.a.bt 2
7744.2.a.bu 2
7744.2.a.bv 2
7744.2.a.bw 2
7744.2.a.bx 2
7744.2.a.by 2
7744.2.a.bz 2
7744.2.a.ca 2
7744.2.a.cb 2
7744.2.a.cc 2
7744.2.a.cd 2
7744.2.a.ce 2
7744.2.a.cf 2
7744.2.a.cg 2
7744.2.a.ch 2
7744.2.a.ci 2
7744.2.a.cj 2
7744.2.a.ck 2
7744.2.a.cl 2
7744.2.a.cm 2
7744.2.a.cn 2
7744.2.a.co 2
7744.2.a.cp 2
7744.2.a.cq 2
7744.2.a.cr 2
7744.2.a.cs 2
7744.2.a.ct 2
7744.2.a.cu 2
7744.2.a.cv 2
7744.2.a.cw 2
7744.2.a.cx 2
7744.2.a.cy 2
7744.2.a.cz 2
7744.2.a.da 2
7744.2.a.db 2
7744.2.a.dc 2
7744.2.a.dd 3
7744.2.a.de 3
7744.2.a.df 3
7744.2.a.dg 3
7744.2.a.dh 4
7744.2.a.di 4
7744.2.a.dj 4
7744.2.a.dk 4
7744.2.a.dl 4
7744.2.a.dm 4
7744.2.a.dn 4
7744.2.a.do 4
7744.2.a.dp 4
7744.2.a.dq 4
7744.2.a.dr 4
7744.2.a.ds 4
7744.2.a.dt 6
7744.2.a.du 6
7744.2.a.dv 6
7744.2.a.dw 6
7744.2.c \(\chi_{7744}(3873, \cdot)\) n/a 218 1
7744.2.e \(\chi_{7744}(7743, \cdot)\) n/a 208 1
7744.2.g \(\chi_{7744}(3871, \cdot)\) n/a 216 1
7744.2.i \(\chi_{7744}(1935, \cdot)\) n/a 416 2
7744.2.j \(\chi_{7744}(1937, \cdot)\) n/a 418 2
7744.2.m \(\chi_{7744}(2689, \cdot)\) n/a 832 4
7744.2.n \(\chi_{7744}(969, \cdot)\) None 0 4
7744.2.q \(\chi_{7744}(967, \cdot)\) None 0 4
7744.2.s \(\chi_{7744}(1183, \cdot)\) n/a 864 4
7744.2.u \(\chi_{7744}(959, \cdot)\) n/a 832 4
7744.2.w \(\chi_{7744}(1697, \cdot)\) n/a 864 4
7744.2.y \(\chi_{7744}(705, \cdot)\) n/a 2620 10
7744.2.ba \(\chi_{7744}(485, \cdot)\) n/a 6904 8
7744.2.bc \(\chi_{7744}(483, \cdot)\) n/a 6848 8
7744.2.bf \(\chi_{7744}(81, \cdot)\) n/a 1664 8
7744.2.bg \(\chi_{7744}(239, \cdot)\) n/a 1664 8
7744.2.bh \(\chi_{7744}(703, \cdot)\) n/a 2620 10
7744.2.bj \(\chi_{7744}(353, \cdot)\) n/a 2640 10
7744.2.bm \(\chi_{7744}(351, \cdot)\) n/a 2640 10
7744.2.bo \(\chi_{7744}(215, \cdot)\) None 0 16
7744.2.br \(\chi_{7744}(9, \cdot)\) None 0 16
7744.2.bu \(\chi_{7744}(177, \cdot)\) n/a 5240 20
7744.2.bv \(\chi_{7744}(175, \cdot)\) n/a 5240 20
7744.2.bw \(\chi_{7744}(257, \cdot)\) n/a 10480 40
7744.2.bx \(\chi_{7744}(403, \cdot)\) n/a 27392 32
7744.2.bz \(\chi_{7744}(245, \cdot)\) n/a 27392 32
7744.2.cb \(\chi_{7744}(87, \cdot)\) None 0 40
7744.2.ce \(\chi_{7744}(89, \cdot)\) None 0 40
7744.2.cg \(\chi_{7744}(95, \cdot)\) n/a 10560 40
7744.2.cj \(\chi_{7744}(97, \cdot)\) n/a 10560 40
7744.2.cl \(\chi_{7744}(63, \cdot)\) n/a 10480 40
7744.2.cm \(\chi_{7744}(43, \cdot)\) n/a 84320 80
7744.2.co \(\chi_{7744}(45, \cdot)\) n/a 84320 80
7744.2.cq \(\chi_{7744}(79, \cdot)\) n/a 20960 80
7744.2.cr \(\chi_{7744}(49, \cdot)\) n/a 20960 80
7744.2.cu \(\chi_{7744}(25, \cdot)\) None 0 160
7744.2.cx \(\chi_{7744}(7, \cdot)\) None 0 160
7744.2.cz \(\chi_{7744}(5, \cdot)\) n/a 337280 320
7744.2.db \(\chi_{7744}(19, \cdot)\) n/a 337280 320

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7744))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7744)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 21}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(352))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(484))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(704))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(968))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1936))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3872))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7744))\)\(^{\oplus 1}\)