Properties

 Label 9610.2 Level 9610 Weight 2 Dimension 843919 Nonzero newspaces 24 Sturm bound 11070720

Defining parameters

 Level: $$N$$ = $$9610 = 2 \cdot 5 \cdot 31^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$24$$ Sturm bound: $$11070720$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(9610))$$.

Total New Old
Modular forms 2778720 843919 1934801
Cusp forms 2756641 843919 1912722
Eisenstein series 22079 0 22079

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(9610))$$

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
9610.2.a $$\chi_{9610}(1, \cdot)$$ 9610.2.a.a 1 1
9610.2.a.b 1
9610.2.a.c 2
9610.2.a.d 2
9610.2.a.e 2
9610.2.a.f 2
9610.2.a.g 2
9610.2.a.h 2
9610.2.a.i 2
9610.2.a.j 2
9610.2.a.k 2
9610.2.a.l 2
9610.2.a.m 2
9610.2.a.n 2
9610.2.a.o 2
9610.2.a.p 2
9610.2.a.q 3
9610.2.a.r 3
9610.2.a.s 3
9610.2.a.t 3
9610.2.a.u 3
9610.2.a.v 3
9610.2.a.w 3
9610.2.a.x 3
9610.2.a.y 3
9610.2.a.z 4
9610.2.a.ba 4
9610.2.a.bb 4
9610.2.a.bc 4
9610.2.a.bd 4
9610.2.a.be 4
9610.2.a.bf 4
9610.2.a.bg 4
9610.2.a.bh 4
9610.2.a.bi 4
9610.2.a.bj 4
9610.2.a.bk 4
9610.2.a.bl 4
9610.2.a.bm 4
9610.2.a.bn 4
9610.2.a.bo 4
9610.2.a.bp 4
9610.2.a.bq 4
9610.2.a.br 4
9610.2.a.bs 4
9610.2.a.bt 4
9610.2.a.bu 4
9610.2.a.bv 4
9610.2.a.bw 4
9610.2.a.bx 4
9610.2.a.by 4
9610.2.a.bz 6
9610.2.a.ca 8
9610.2.a.cb 8
9610.2.a.cc 8
9610.2.a.cd 8
9610.2.a.ce 12
9610.2.a.cf 12
9610.2.a.cg 12
9610.2.a.ch 12
9610.2.a.ci 16
9610.2.a.cj 24
9610.2.a.ck 24
9610.2.b $$\chi_{9610}(7689, \cdot)$$ n/a 464 1
9610.2.e $$\chi_{9610}(521, \cdot)$$ n/a 616 2
9610.2.f $$\chi_{9610}(3843, \cdot)$$ n/a 928 2
9610.2.h $$\chi_{9610}(531, \cdot)$$ n/a 1248 4
9610.2.k $$\chi_{9610}(439, \cdot)$$ n/a 928 2
9610.2.n $$\chi_{9610}(1349, \cdot)$$ n/a 1856 4
9610.2.p $$\chi_{9610}(1483, \cdot)$$ n/a 1856 4
9610.2.q $$\chi_{9610}(3221, \cdot)$$ n/a 2464 8
9610.2.s $$\chi_{9610}(333, \cdot)$$ n/a 3712 8
9610.2.t $$\chi_{9610}(1299, \cdot)$$ n/a 3712 8
9610.2.w $$\chi_{9610}(311, \cdot)$$ n/a 9840 30
9610.2.x $$\chi_{9610}(117, \cdot)$$ n/a 7424 16
9610.2.bb $$\chi_{9610}(249, \cdot)$$ n/a 14880 30
9610.2.bc $$\chi_{9610}(191, \cdot)$$ n/a 19920 60
9610.2.be $$\chi_{9610}(123, \cdot)$$ n/a 29760 60
9610.2.bf $$\chi_{9610}(101, \cdot)$$ n/a 39360 120
9610.2.bg $$\chi_{9610}(129, \cdot)$$ n/a 29760 60
9610.2.bj $$\chi_{9610}(39, \cdot)$$ n/a 59520 120
9610.2.bm $$\chi_{9610}(37, \cdot)$$ n/a 59520 120
9610.2.bo $$\chi_{9610}(41, \cdot)$$ n/a 79680 240
9610.2.bp $$\chi_{9610}(23, \cdot)$$ n/a 119040 240
9610.2.bt $$\chi_{9610}(9, \cdot)$$ n/a 119040 240
9610.2.bv $$\chi_{9610}(3, \cdot)$$ n/a 238080 480

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

Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(9610))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(9610)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(31))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(62))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(155))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(310))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(961))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1922))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4805))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9610))$$$$^{\oplus 1}$$