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Properties

Label 9024.2
Level 9024
Weight 2
Dimension 951012
Nonzero newspaces 32
Sturm bound 9043968

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Defining parameters

Level: \( N \) = \( 9024 = 2^{6} \cdot 3 \cdot 47 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(9043968\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9024))\).

Total New Old
Modular forms 2274240 954972 1319268
Cusp forms 2247745 951012 1296733
Eisenstein series 26495 3960 22535

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9024))\)

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
9024.2.a \(\chi_{9024}(1, \cdot)\) 9024.2.a.a 1 1
9024.2.a.b 1
9024.2.a.c 1
9024.2.a.d 1
9024.2.a.e 1
9024.2.a.f 1
9024.2.a.g 1
9024.2.a.h 1
9024.2.a.i 1
9024.2.a.j 1
9024.2.a.k 1
9024.2.a.l 1
9024.2.a.m 1
9024.2.a.n 1
9024.2.a.o 1
9024.2.a.p 1
9024.2.a.q 1
9024.2.a.r 1
9024.2.a.s 1
9024.2.a.t 1
9024.2.a.u 1
9024.2.a.v 1
9024.2.a.w 1
9024.2.a.x 1
9024.2.a.y 1
9024.2.a.z 1
9024.2.a.ba 1
9024.2.a.bb 1
9024.2.a.bc 1
9024.2.a.bd 1
9024.2.a.be 1
9024.2.a.bf 1
9024.2.a.bg 1
9024.2.a.bh 1
9024.2.a.bi 1
9024.2.a.bj 1
9024.2.a.bk 1
9024.2.a.bl 1
9024.2.a.bm 1
9024.2.a.bn 1
9024.2.a.bo 1
9024.2.a.bp 1
9024.2.a.bq 1
9024.2.a.br 1
9024.2.a.bs 1
9024.2.a.bt 1
9024.2.a.bu 1
9024.2.a.bv 1
9024.2.a.bw 1
9024.2.a.bx 1
9024.2.a.by 2
9024.2.a.bz 2
9024.2.a.ca 2
9024.2.a.cb 2
9024.2.a.cc 2
9024.2.a.cd 2
9024.2.a.ce 2
9024.2.a.cf 2
9024.2.a.cg 2
9024.2.a.ch 2
9024.2.a.ci 3
9024.2.a.cj 3
9024.2.a.ck 3
9024.2.a.cl 3
9024.2.a.cm 3
9024.2.a.cn 3
9024.2.a.co 3
9024.2.a.cp 3
9024.2.a.cq 3
9024.2.a.cr 3
9024.2.a.cs 3
9024.2.a.ct 3
9024.2.a.cu 3
9024.2.a.cv 3
9024.2.a.cw 3
9024.2.a.cx 3
9024.2.a.cy 4
9024.2.a.cz 4
9024.2.a.da 4
9024.2.a.db 4
9024.2.a.dc 5
9024.2.a.dd 5
9024.2.a.de 6
9024.2.a.df 6
9024.2.a.dg 6
9024.2.a.dh 6
9024.2.a.di 8
9024.2.a.dj 8
9024.2.c \(\chi_{9024}(3007, \cdot)\) n/a 192 1
9024.2.e \(\chi_{9024}(4607, \cdot)\) n/a 368 1
9024.2.g \(\chi_{9024}(4513, \cdot)\) n/a 184 1
9024.2.i \(\chi_{9024}(5921, \cdot)\) n/a 384 1
9024.2.k \(\chi_{9024}(95, \cdot)\) n/a 368 1
9024.2.m \(\chi_{9024}(7519, \cdot)\) n/a 192 1
9024.2.o \(\chi_{9024}(1409, \cdot)\) n/a 380 1
9024.2.q \(\chi_{9024}(3665, \cdot)\) n/a 760 2
9024.2.s \(\chi_{9024}(2257, \cdot)\) n/a 368 2
9024.2.u \(\chi_{9024}(2351, \cdot)\) n/a 736 2
9024.2.w \(\chi_{9024}(751, \cdot)\) n/a 384 2
9024.2.ba \(\chi_{9024}(1129, \cdot)\) None 0 4
9024.2.bb \(\chi_{9024}(1879, \cdot)\) None 0 4
9024.2.bc \(\chi_{9024}(281, \cdot)\) None 0 4
9024.2.bd \(\chi_{9024}(1223, \cdot)\) None 0 4
9024.2.bi \(\chi_{9024}(565, \cdot)\) n/a 5888 8
9024.2.bj \(\chi_{9024}(187, \cdot)\) n/a 6144 8
9024.2.bk \(\chi_{9024}(659, \cdot)\) n/a 11776 8
9024.2.bl \(\chi_{9024}(845, \cdot)\) n/a 12256 8
9024.2.bo \(\chi_{9024}(385, \cdot)\) n/a 4224 22
9024.2.bq \(\chi_{9024}(257, \cdot)\) n/a 8360 22
9024.2.bs \(\chi_{9024}(31, \cdot)\) n/a 4224 22
9024.2.bu \(\chi_{9024}(479, \cdot)\) n/a 8448 22
9024.2.bw \(\chi_{9024}(161, \cdot)\) n/a 8448 22
9024.2.by \(\chi_{9024}(97, \cdot)\) n/a 4224 22
9024.2.ca \(\chi_{9024}(191, \cdot)\) n/a 8360 22
9024.2.cc \(\chi_{9024}(127, \cdot)\) n/a 4224 22
9024.2.cf \(\chi_{9024}(367, \cdot)\) n/a 8448 44
9024.2.ch \(\chi_{9024}(143, \cdot)\) n/a 16720 44
9024.2.cj \(\chi_{9024}(49, \cdot)\) n/a 8448 44
9024.2.cl \(\chi_{9024}(113, \cdot)\) n/a 16720 44
9024.2.co \(\chi_{9024}(71, \cdot)\) None 0 88
9024.2.cp \(\chi_{9024}(41, \cdot)\) None 0 88
9024.2.cq \(\chi_{9024}(151, \cdot)\) None 0 88
9024.2.cr \(\chi_{9024}(25, \cdot)\) None 0 88
9024.2.cw \(\chi_{9024}(59, \cdot)\) n/a 269632 176
9024.2.cx \(\chi_{9024}(5, \cdot)\) n/a 269632 176
9024.2.cy \(\chi_{9024}(37, \cdot)\) n/a 135168 176
9024.2.cz \(\chi_{9024}(19, \cdot)\) n/a 135168 176

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9024))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9024)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(47))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(94))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(141))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(188))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(282))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(376))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(564))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(752))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1128))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1504))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2256))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3008))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4512))\)\(^{\oplus 2}\)