Properties

Label 5415.2
Level 5415
Weight 2
Dimension 708012
Nonzero newspaces 36
Sturm bound 4158720

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Defining parameters

Level: \( N \) = \( 5415 = 3 \cdot 5 \cdot 19^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(4158720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5415))\).

Total New Old
Modular forms 1047744 713636 334108
Cusp forms 1031617 708012 323605
Eisenstein series 16127 5624 10503

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5415))\)

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
5415.2.a \(\chi_{5415}(1, \cdot)\) 5415.2.a.a 1 1
5415.2.a.b 1
5415.2.a.c 1
5415.2.a.d 1
5415.2.a.e 1
5415.2.a.f 1
5415.2.a.g 1
5415.2.a.h 1
5415.2.a.i 1
5415.2.a.j 1
5415.2.a.k 1
5415.2.a.l 1
5415.2.a.m 2
5415.2.a.n 2
5415.2.a.o 2
5415.2.a.p 2
5415.2.a.q 2
5415.2.a.r 2
5415.2.a.s 2
5415.2.a.t 2
5415.2.a.u 2
5415.2.a.v 2
5415.2.a.w 3
5415.2.a.x 3
5415.2.a.y 5
5415.2.a.z 5
5415.2.a.ba 6
5415.2.a.bb 6
5415.2.a.bc 6
5415.2.a.bd 6
5415.2.a.be 6
5415.2.a.bf 6
5415.2.a.bg 6
5415.2.a.bh 6
5415.2.a.bi 6
5415.2.a.bj 6
5415.2.a.bk 9
5415.2.a.bl 9
5415.2.a.bm 12
5415.2.a.bn 12
5415.2.a.bo 12
5415.2.a.bp 12
5415.2.a.bq 12
5415.2.a.br 12
5415.2.a.bs 15
5415.2.a.bt 15
5415.2.b \(\chi_{5415}(5414, \cdot)\) n/a 648 1
5415.2.c \(\chi_{5415}(1084, \cdot)\) n/a 340 1
5415.2.h \(\chi_{5415}(4331, \cdot)\) n/a 452 1
5415.2.i \(\chi_{5415}(2956, \cdot)\) n/a 456 2
5415.2.k \(\chi_{5415}(362, \cdot)\) n/a 1296 2
5415.2.m \(\chi_{5415}(2887, \cdot)\) n/a 680 2
5415.2.p \(\chi_{5415}(791, \cdot)\) n/a 904 2
5415.2.q \(\chi_{5415}(1874, \cdot)\) n/a 1296 2
5415.2.r \(\chi_{5415}(4039, \cdot)\) n/a 680 2
5415.2.u \(\chi_{5415}(1111, \cdot)\) n/a 1356 6
5415.2.v \(\chi_{5415}(68, \cdot)\) n/a 2592 4
5415.2.x \(\chi_{5415}(1513, \cdot)\) n/a 1360 4
5415.2.z \(\chi_{5415}(116, \cdot)\) n/a 2724 6
5415.2.be \(\chi_{5415}(784, \cdot)\) n/a 2040 6
5415.2.bf \(\chi_{5415}(299, \cdot)\) n/a 3888 6
5415.2.bg \(\chi_{5415}(286, \cdot)\) n/a 4536 18
5415.2.bi \(\chi_{5415}(127, \cdot)\) n/a 4080 12
5415.2.bj \(\chi_{5415}(62, \cdot)\) n/a 7776 12
5415.2.bl \(\chi_{5415}(56, \cdot)\) n/a 9144 18
5415.2.bq \(\chi_{5415}(229, \cdot)\) n/a 6840 18
5415.2.br \(\chi_{5415}(284, \cdot)\) n/a 13608 18
5415.2.bs \(\chi_{5415}(106, \cdot)\) n/a 9072 36
5415.2.bt \(\chi_{5415}(37, \cdot)\) n/a 13680 36
5415.2.bv \(\chi_{5415}(77, \cdot)\) n/a 27216 36
5415.2.bz \(\chi_{5415}(49, \cdot)\) n/a 13680 36
5415.2.ca \(\chi_{5415}(164, \cdot)\) n/a 27216 36
5415.2.cb \(\chi_{5415}(221, \cdot)\) n/a 18288 36
5415.2.ce \(\chi_{5415}(16, \cdot)\) n/a 27432 108
5415.2.cg \(\chi_{5415}(88, \cdot)\) n/a 27360 72
5415.2.ci \(\chi_{5415}(83, \cdot)\) n/a 54432 72
5415.2.cj \(\chi_{5415}(14, \cdot)\) n/a 81648 108
5415.2.ck \(\chi_{5415}(4, \cdot)\) n/a 41040 108
5415.2.cp \(\chi_{5415}(41, \cdot)\) n/a 54648 108
5415.2.cr \(\chi_{5415}(17, \cdot)\) n/a 163296 216
5415.2.cs \(\chi_{5415}(13, \cdot)\) n/a 82080 216

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5415))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5415)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(285))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1083))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1805))\)\(^{\oplus 2}\)