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Properties

Label 9306.2
Level 9306
Weight 2
Dimension 618230
Nonzero newspaces 32
Sturm bound 9538560

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Defining parameters

Level: \( N \) = \( 9306 = 2 \cdot 3^{2} \cdot 11 \cdot 47 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(9538560\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9306))\).

Total New Old
Modular forms 2399360 618230 1781130
Cusp forms 2369921 618230 1751691
Eisenstein series 29439 0 29439

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9306))\)

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
9306.2.a \(\chi_{9306}(1, \cdot)\) 9306.2.a.a 1 1
9306.2.a.b 1
9306.2.a.c 1
9306.2.a.d 1
9306.2.a.e 1
9306.2.a.f 1
9306.2.a.g 1
9306.2.a.h 1
9306.2.a.i 1
9306.2.a.j 1
9306.2.a.k 1
9306.2.a.l 1
9306.2.a.m 1
9306.2.a.n 1
9306.2.a.o 1
9306.2.a.p 1
9306.2.a.q 1
9306.2.a.r 2
9306.2.a.s 2
9306.2.a.t 2
9306.2.a.u 3
9306.2.a.v 3
9306.2.a.w 3
9306.2.a.x 3
9306.2.a.y 4
9306.2.a.z 4
9306.2.a.ba 4
9306.2.a.bb 4
9306.2.a.bc 4
9306.2.a.bd 5
9306.2.a.be 5
9306.2.a.bf 5
9306.2.a.bg 5
9306.2.a.bh 6
9306.2.a.bi 6
9306.2.a.bj 7
9306.2.a.bk 7
9306.2.a.bl 7
9306.2.a.bm 7
9306.2.a.bn 7
9306.2.a.bo 7
9306.2.a.bp 8
9306.2.a.bq 9
9306.2.a.br 11
9306.2.a.bs 11
9306.2.a.bt 11
9306.2.a.bu 11
9306.2.b \(\chi_{9306}(3761, \cdot)\) n/a 184 1
9306.2.c \(\chi_{9306}(7237, \cdot)\) n/a 240 1
9306.2.h \(\chi_{9306}(7613, \cdot)\) n/a 160 1
9306.2.i \(\chi_{9306}(3103, \cdot)\) n/a 920 2
9306.2.j \(\chi_{9306}(2539, \cdot)\) n/a 920 4
9306.2.k \(\chi_{9306}(1409, \cdot)\) n/a 960 2
9306.2.p \(\chi_{9306}(1033, \cdot)\) n/a 1152 2
9306.2.q \(\chi_{9306}(659, \cdot)\) n/a 1104 2
9306.2.r \(\chi_{9306}(845, \cdot)\) n/a 768 4
9306.2.w \(\chi_{9306}(469, \cdot)\) n/a 960 4
9306.2.x \(\chi_{9306}(1223, \cdot)\) n/a 736 4
9306.2.y \(\chi_{9306}(565, \cdot)\) n/a 4416 8
9306.2.z \(\chi_{9306}(397, \cdot)\) n/a 4400 22
9306.2.ba \(\chi_{9306}(95, \cdot)\) n/a 4416 8
9306.2.bb \(\chi_{9306}(1597, \cdot)\) n/a 4608 8
9306.2.bg \(\chi_{9306}(1127, \cdot)\) n/a 4608 8
9306.2.bh \(\chi_{9306}(287, \cdot)\) n/a 3520 22
9306.2.bm \(\chi_{9306}(109, \cdot)\) n/a 5280 22
9306.2.bn \(\chi_{9306}(197, \cdot)\) n/a 4224 22
9306.2.bo \(\chi_{9306}(331, \cdot)\) n/a 21120 44
9306.2.bp \(\chi_{9306}(37, \cdot)\) n/a 21120 88
9306.2.bq \(\chi_{9306}(65, \cdot)\) n/a 25344 44
9306.2.br \(\chi_{9306}(43, \cdot)\) n/a 25344 44
9306.2.bw \(\chi_{9306}(23, \cdot)\) n/a 21120 44
9306.2.bx \(\chi_{9306}(17, \cdot)\) n/a 16896 88
9306.2.by \(\chi_{9306}(19, \cdot)\) n/a 21120 88
9306.2.cd \(\chi_{9306}(125, \cdot)\) n/a 16896 88
9306.2.ce \(\chi_{9306}(25, \cdot)\) n/a 101376 176
9306.2.cf \(\chi_{9306}(5, \cdot)\) n/a 101376 176
9306.2.ck \(\chi_{9306}(13, \cdot)\) n/a 101376 176
9306.2.cl \(\chi_{9306}(83, \cdot)\) n/a 101376 176

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9306))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9306)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(47))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(94))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(141))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(282))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(423))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(517))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(846))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1034))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1551))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3102))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4653))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9306))\)\(^{\oplus 1}\)