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Properties

Label 7260.2
Level 7260
Weight 2
Dimension 548134
Nonzero newspaces 48
Sturm bound 5575680

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Defining parameters

Level: \( N \) = \( 7260 = 2^{2} \cdot 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(5575680\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7260))\).

Total New Old
Modular forms 1406720 551502 855218
Cusp forms 1381121 548134 832987
Eisenstein series 25599 3368 22231

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7260))\)

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
7260.2.a \(\chi_{7260}(1, \cdot)\) 7260.2.a.a 1 1
7260.2.a.b 1
7260.2.a.c 1
7260.2.a.d 1
7260.2.a.e 1
7260.2.a.f 1
7260.2.a.g 1
7260.2.a.h 1
7260.2.a.i 1
7260.2.a.j 1
7260.2.a.k 1
7260.2.a.l 1
7260.2.a.m 1
7260.2.a.n 1
7260.2.a.o 1
7260.2.a.p 1
7260.2.a.q 1
7260.2.a.r 1
7260.2.a.s 1
7260.2.a.t 1
7260.2.a.u 2
7260.2.a.v 2
7260.2.a.w 2
7260.2.a.x 2
7260.2.a.y 2
7260.2.a.z 2
7260.2.a.ba 4
7260.2.a.bb 4
7260.2.a.bc 4
7260.2.a.bd 4
7260.2.a.be 4
7260.2.a.bf 4
7260.2.a.bg 4
7260.2.a.bh 4
7260.2.a.bi 4
7260.2.a.bj 4
7260.2.c \(\chi_{7260}(5809, \cdot)\) n/a 110 1
7260.2.d \(\chi_{7260}(5081, \cdot)\) n/a 144 1
7260.2.f \(\chi_{7260}(1211, \cdot)\) n/a 872 1
7260.2.i \(\chi_{7260}(2419, \cdot)\) n/a 648 1
7260.2.k \(\chi_{7260}(3871, \cdot)\) n/a 432 1
7260.2.l \(\chi_{7260}(7019, \cdot)\) n/a 1272 1
7260.2.n \(\chi_{7260}(3629, \cdot)\) n/a 216 1
7260.2.q \(\chi_{7260}(2903, \cdot)\) n/a 2528 2
7260.2.t \(\chi_{7260}(1937, \cdot)\) n/a 436 2
7260.2.u \(\chi_{7260}(727, \cdot)\) n/a 1308 2
7260.2.x \(\chi_{7260}(1693, \cdot)\) n/a 216 2
7260.2.y \(\chi_{7260}(4141, \cdot)\) n/a 288 4
7260.2.bb \(\chi_{7260}(3869, \cdot)\) n/a 864 4
7260.2.bd \(\chi_{7260}(3899, \cdot)\) n/a 5056 4
7260.2.be \(\chi_{7260}(4111, \cdot)\) n/a 1728 4
7260.2.bg \(\chi_{7260}(2659, \cdot)\) n/a 2592 4
7260.2.bj \(\chi_{7260}(251, \cdot)\) n/a 3456 4
7260.2.bl \(\chi_{7260}(161, \cdot)\) n/a 576 4
7260.2.bm \(\chi_{7260}(2689, \cdot)\) n/a 432 4
7260.2.bo \(\chi_{7260}(661, \cdot)\) n/a 880 10
7260.2.bp \(\chi_{7260}(457, \cdot)\) n/a 864 8
7260.2.bs \(\chi_{7260}(487, \cdot)\) n/a 5184 8
7260.2.bt \(\chi_{7260}(977, \cdot)\) n/a 1728 8
7260.2.bw \(\chi_{7260}(887, \cdot)\) n/a 10112 8
7260.2.bz \(\chi_{7260}(329, \cdot)\) n/a 2640 10
7260.2.cb \(\chi_{7260}(419, \cdot)\) n/a 15760 10
7260.2.cc \(\chi_{7260}(571, \cdot)\) n/a 5280 10
7260.2.ce \(\chi_{7260}(439, \cdot)\) n/a 7920 10
7260.2.ch \(\chi_{7260}(551, \cdot)\) n/a 10560 10
7260.2.cj \(\chi_{7260}(461, \cdot)\) n/a 1760 10
7260.2.ck \(\chi_{7260}(529, \cdot)\) n/a 1320 10
7260.2.cm \(\chi_{7260}(373, \cdot)\) n/a 2640 20
7260.2.cp \(\chi_{7260}(67, \cdot)\) n/a 15840 20
7260.2.cq \(\chi_{7260}(353, \cdot)\) n/a 5280 20
7260.2.ct \(\chi_{7260}(263, \cdot)\) n/a 31520 20
7260.2.cu \(\chi_{7260}(181, \cdot)\) n/a 3520 40
7260.2.cw \(\chi_{7260}(49, \cdot)\) n/a 5280 40
7260.2.cx \(\chi_{7260}(41, \cdot)\) n/a 7040 40
7260.2.cz \(\chi_{7260}(71, \cdot)\) n/a 42240 40
7260.2.dc \(\chi_{7260}(19, \cdot)\) n/a 31680 40
7260.2.de \(\chi_{7260}(151, \cdot)\) n/a 21120 40
7260.2.df \(\chi_{7260}(59, \cdot)\) n/a 63040 40
7260.2.dh \(\chi_{7260}(29, \cdot)\) n/a 10560 40
7260.2.dk \(\chi_{7260}(83, \cdot)\) n/a 126080 80
7260.2.dn \(\chi_{7260}(53, \cdot)\) n/a 21120 80
7260.2.do \(\chi_{7260}(103, \cdot)\) n/a 63360 80
7260.2.dr \(\chi_{7260}(13, \cdot)\) n/a 10560 80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7260))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7260)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(330))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(484))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(605))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(660))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(726))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1452))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1815))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2420))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3630))\)\(^{\oplus 2}\)