Properties

Label 7220.2
Level 7220
Weight 2
Dimension 826485
Nonzero newspaces 36
Sturm bound 6238080

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Defining parameters

Level: \( N \) = \( 7220 = 2^{2} \cdot 5 \cdot 19^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(6238080\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7220))\).

Total New Old
Modular forms 1569600 832109 737491
Cusp forms 1549441 826485 722956
Eisenstein series 20159 5624 14535

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7220))\)

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
7220.2.a \(\chi_{7220}(1, \cdot)\) 7220.2.a.a 1 1
7220.2.a.b 1
7220.2.a.c 1
7220.2.a.d 1
7220.2.a.e 1
7220.2.a.f 1
7220.2.a.g 1
7220.2.a.h 2
7220.2.a.i 2
7220.2.a.j 2
7220.2.a.k 2
7220.2.a.l 2
7220.2.a.m 2
7220.2.a.n 3
7220.2.a.o 3
7220.2.a.p 4
7220.2.a.q 4
7220.2.a.r 4
7220.2.a.s 8
7220.2.a.t 8
7220.2.a.u 8
7220.2.a.v 9
7220.2.a.w 9
7220.2.a.x 9
7220.2.a.y 9
7220.2.a.z 16
7220.2.c \(\chi_{7220}(2889, \cdot)\) n/a 170 1
7220.2.d \(\chi_{7220}(7219, \cdot)\) n/a 988 1
7220.2.f \(\chi_{7220}(4331, \cdot)\) n/a 680 1
7220.2.i \(\chi_{7220}(3541, \cdot)\) n/a 224 2
7220.2.k \(\chi_{7220}(723, \cdot)\) n/a 1978 2
7220.2.l \(\chi_{7220}(5053, \cdot)\) n/a 340 2
7220.2.n \(\chi_{7220}(791, \cdot)\) n/a 1360 2
7220.2.r \(\chi_{7220}(429, \cdot)\) n/a 340 2
7220.2.s \(\chi_{7220}(2459, \cdot)\) n/a 1976 2
7220.2.u \(\chi_{7220}(821, \cdot)\) n/a 684 6
7220.2.v \(\chi_{7220}(4263, \cdot)\) n/a 3952 4
7220.2.y \(\chi_{7220}(293, \cdot)\) n/a 680 4
7220.2.bb \(\chi_{7220}(299, \cdot)\) n/a 5928 6
7220.2.bd \(\chi_{7220}(389, \cdot)\) n/a 1020 6
7220.2.be \(\chi_{7220}(1571, \cdot)\) n/a 4080 6
7220.2.bg \(\chi_{7220}(381, \cdot)\) n/a 2304 18
7220.2.bi \(\chi_{7220}(333, \cdot)\) n/a 2040 12
7220.2.bk \(\chi_{7220}(423, \cdot)\) n/a 11856 12
7220.2.bn \(\chi_{7220}(151, \cdot)\) n/a 13680 18
7220.2.bp \(\chi_{7220}(379, \cdot)\) n/a 20448 18
7220.2.bq \(\chi_{7220}(229, \cdot)\) n/a 3420 18
7220.2.bs \(\chi_{7220}(121, \cdot)\) n/a 4608 36
7220.2.bu \(\chi_{7220}(37, \cdot)\) n/a 6840 36
7220.2.bv \(\chi_{7220}(267, \cdot)\) n/a 40896 36
7220.2.by \(\chi_{7220}(179, \cdot)\) n/a 40896 36
7220.2.bz \(\chi_{7220}(49, \cdot)\) n/a 6840 36
7220.2.cd \(\chi_{7220}(31, \cdot)\) n/a 27360 36
7220.2.ce \(\chi_{7220}(61, \cdot)\) n/a 13608 108
7220.2.cf \(\chi_{7220}(217, \cdot)\) n/a 13680 72
7220.2.ci \(\chi_{7220}(7, \cdot)\) n/a 81792 72
7220.2.ck \(\chi_{7220}(51, \cdot)\) n/a 82080 108
7220.2.cl \(\chi_{7220}(9, \cdot)\) n/a 20520 108
7220.2.cn \(\chi_{7220}(59, \cdot)\) n/a 122688 108
7220.2.cq \(\chi_{7220}(23, \cdot)\) n/a 245376 216
7220.2.cs \(\chi_{7220}(13, \cdot)\) n/a 41040 216

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7220))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7220)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(190))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(380))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(722))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1444))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1805))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3610))\)\(^{\oplus 2}\)