Properties

Label 9522.2
Level 9522
Weight 2
Dimension 660860
Nonzero newspaces 16
Sturm bound 10055232

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Defining parameters

Level: \( N \) = \( 9522 = 2 \cdot 3^{2} \cdot 23^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(10055232\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9522))\).

Total New Old
Modular forms 2525776 660860 1864916
Cusp forms 2501841 660860 1840981
Eisenstein series 23935 0 23935

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9522))\)

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
9522.2.a \(\chi_{9522}(1, \cdot)\) 9522.2.a.a 1 1
9522.2.a.b 1
9522.2.a.c 1
9522.2.a.d 1
9522.2.a.e 1
9522.2.a.f 1
9522.2.a.g 1
9522.2.a.h 1
9522.2.a.i 1
9522.2.a.j 1
9522.2.a.k 1
9522.2.a.l 1
9522.2.a.m 1
9522.2.a.n 1
9522.2.a.o 1
9522.2.a.p 1
9522.2.a.q 2
9522.2.a.r 2
9522.2.a.s 2
9522.2.a.t 2
9522.2.a.u 2
9522.2.a.v 2
9522.2.a.w 2
9522.2.a.x 2
9522.2.a.y 2
9522.2.a.z 2
9522.2.a.ba 2
9522.2.a.bb 2
9522.2.a.bc 2
9522.2.a.bd 2
9522.2.a.be 2
9522.2.a.bf 2
9522.2.a.bg 2
9522.2.a.bh 2
9522.2.a.bi 2
9522.2.a.bj 2
9522.2.a.bk 2
9522.2.a.bl 4
9522.2.a.bm 4
9522.2.a.bn 4
9522.2.a.bo 4
9522.2.a.bp 5
9522.2.a.bq 5
9522.2.a.br 5
9522.2.a.bs 5
9522.2.a.bt 5
9522.2.a.bu 5
9522.2.a.bv 5
9522.2.a.bw 5
9522.2.a.bx 5
9522.2.a.by 5
9522.2.a.bz 5
9522.2.a.ca 5
9522.2.a.cb 6
9522.2.a.cc 6
9522.2.a.cd 8
9522.2.a.ce 8
9522.2.a.cf 8
9522.2.a.cg 10
9522.2.a.ch 10
9522.2.a.ci 10
9522.2.a.cj 10
9522.2.d \(\chi_{9522}(9521, \cdot)\) n/a 168 1
9522.2.e \(\chi_{9522}(3175, \cdot)\) n/a 1010 2
9522.2.f \(\chi_{9522}(3173, \cdot)\) n/a 1008 2
9522.2.i \(\chi_{9522}(487, \cdot)\) n/a 2100 10
9522.2.j \(\chi_{9522}(359, \cdot)\) n/a 1680 10
9522.2.m \(\chi_{9522}(415, \cdot)\) n/a 5060 22
9522.2.n \(\chi_{9522}(1705, \cdot)\) n/a 10080 20
9522.2.o \(\chi_{9522}(413, \cdot)\) n/a 4048 22
9522.2.t \(\chi_{9522}(263, \cdot)\) n/a 10080 20
9522.2.u \(\chi_{9522}(139, \cdot)\) n/a 24288 44
9522.2.x \(\chi_{9522}(137, \cdot)\) n/a 24288 44
9522.2.y \(\chi_{9522}(55, \cdot)\) n/a 50600 220
9522.2.bb \(\chi_{9522}(17, \cdot)\) n/a 40480 220
9522.2.bc \(\chi_{9522}(13, \cdot)\) n/a 242880 440
9522.2.bd \(\chi_{9522}(5, \cdot)\) n/a 242880 440

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9522))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9522)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(207))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(414))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(529))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1058))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1587))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3174))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4761))\)\(^{\oplus 2}\)