Properties

Label 9216.2
Level 9216
Weight 2
Dimension 1048464
Nonzero newspaces 32
Sturm bound 9437184

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Defining parameters

Level: \( N \) = \( 9216 = 2^{10} \cdot 3^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(9437184\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9216))\).

Total New Old
Modular forms 2372608 1052784 1319824
Cusp forms 2345985 1048464 1297521
Eisenstein series 26623 4320 22303

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9216))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
9216.2.a \(\chi_{9216}(1, \cdot)\) 9216.2.a.a 2 1
9216.2.a.b 2
9216.2.a.c 2
9216.2.a.d 2
9216.2.a.e 2
9216.2.a.f 2
9216.2.a.g 2
9216.2.a.h 2
9216.2.a.i 2
9216.2.a.j 2
9216.2.a.k 2
9216.2.a.l 2
9216.2.a.m 2
9216.2.a.n 2
9216.2.a.o 2
9216.2.a.p 2
9216.2.a.q 2
9216.2.a.r 2
9216.2.a.s 2
9216.2.a.t 2
9216.2.a.u 2
9216.2.a.v 2
9216.2.a.w 4
9216.2.a.x 4
9216.2.a.y 4
9216.2.a.z 4
9216.2.a.ba 4
9216.2.a.bb 4
9216.2.a.bc 4
9216.2.a.bd 4
9216.2.a.be 4
9216.2.a.bf 4
9216.2.a.bg 4
9216.2.a.bh 4
9216.2.a.bi 4
9216.2.a.bj 4
9216.2.a.bk 4
9216.2.a.bl 4
9216.2.a.bm 4
9216.2.a.bn 4
9216.2.a.bo 4
9216.2.a.bp 4
9216.2.a.bq 8
9216.2.a.br 8
9216.2.a.bs 8
9216.2.a.bt 8
9216.2.c \(\chi_{9216}(9215, \cdot)\) n/a 128 1
9216.2.d \(\chi_{9216}(4609, \cdot)\) n/a 156 1
9216.2.f \(\chi_{9216}(4607, \cdot)\) n/a 128 1
9216.2.i \(\chi_{9216}(3073, \cdot)\) n/a 752 2
9216.2.k \(\chi_{9216}(2305, \cdot)\) n/a 312 2
9216.2.l \(\chi_{9216}(2303, \cdot)\) n/a 256 2
9216.2.p \(\chi_{9216}(1535, \cdot)\) n/a 752 2
9216.2.r \(\chi_{9216}(1537, \cdot)\) n/a 752 2
9216.2.s \(\chi_{9216}(3071, \cdot)\) n/a 752 2
9216.2.v \(\chi_{9216}(1153, \cdot)\) n/a 640 4
9216.2.w \(\chi_{9216}(1151, \cdot)\) n/a 512 4
9216.2.y \(\chi_{9216}(767, \cdot)\) n/a 1504 4
9216.2.bb \(\chi_{9216}(769, \cdot)\) n/a 1504 4
9216.2.bd \(\chi_{9216}(577, \cdot)\) n/a 1248 8
9216.2.be \(\chi_{9216}(575, \cdot)\) n/a 1024 8
9216.2.bg \(\chi_{9216}(385, \cdot)\) n/a 3072 8
9216.2.bj \(\chi_{9216}(383, \cdot)\) n/a 3072 8
9216.2.bl \(\chi_{9216}(289, \cdot)\) n/a 2528 16
9216.2.bm \(\chi_{9216}(287, \cdot)\) n/a 2048 16
9216.2.bp \(\chi_{9216}(191, \cdot)\) n/a 6016 16
9216.2.bq \(\chi_{9216}(193, \cdot)\) n/a 6016 16
9216.2.bt \(\chi_{9216}(145, \cdot)\) n/a 5088 32
9216.2.bu \(\chi_{9216}(143, \cdot)\) n/a 4096 32
9216.2.bw \(\chi_{9216}(95, \cdot)\) n/a 12160 32
9216.2.bz \(\chi_{9216}(97, \cdot)\) n/a 12160 32
9216.2.cb \(\chi_{9216}(73, \cdot)\) None 0 64
9216.2.cc \(\chi_{9216}(71, \cdot)\) None 0 64
9216.2.ce \(\chi_{9216}(49, \cdot)\) n/a 24448 64
9216.2.ch \(\chi_{9216}(47, \cdot)\) n/a 24448 64
9216.2.cj \(\chi_{9216}(37, \cdot)\) n/a 81792 128
9216.2.ck \(\chi_{9216}(35, \cdot)\) n/a 65536 128
9216.2.cn \(\chi_{9216}(23, \cdot)\) None 0 128
9216.2.co \(\chi_{9216}(25, \cdot)\) None 0 128
9216.2.cq \(\chi_{9216}(11, \cdot)\) n/a 392704 256
9216.2.ct \(\chi_{9216}(13, \cdot)\) n/a 392704 256

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9216))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9216)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 21}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(256))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(384))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(512))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(576))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(768))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1024))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1152))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1536))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2304))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3072))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4608))\)\(^{\oplus 2}\)