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Properties

Label 10470.2
Level 10470
Weight 2
Dimension 669885
Nonzero newspaces 40
Sturm bound 11692800

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Defining parameters

Level: \( N \) = \( 10470 = 2 \cdot 3 \cdot 5 \cdot 349 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(11692800\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(10470))\).

Total New Old
Modular forms 2934336 669885 2264451
Cusp forms 2912065 669885 2242180
Eisenstein series 22271 0 22271

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(10470))\)

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
10470.2.a \(\chi_{10470}(1, \cdot)\) 10470.2.a.a 1 1
10470.2.a.b 1
10470.2.a.c 1
10470.2.a.d 1
10470.2.a.e 1
10470.2.a.f 2
10470.2.a.g 5
10470.2.a.h 5
10470.2.a.i 10
10470.2.a.j 12
10470.2.a.k 12
10470.2.a.l 12
10470.2.a.m 12
10470.2.a.n 14
10470.2.a.o 14
10470.2.a.p 14
10470.2.a.q 15
10470.2.a.r 16
10470.2.a.s 16
10470.2.a.t 17
10470.2.a.u 17
10470.2.a.v 17
10470.2.a.w 18
10470.2.c \(\chi_{10470}(2791, \cdot)\) n/a 236 1
10470.2.e \(\chi_{10470}(4189, \cdot)\) n/a 348 1
10470.2.g \(\chi_{10470}(6979, \cdot)\) n/a 348 1
10470.2.i \(\chi_{10470}(3961, \cdot)\) n/a 464 2
10470.2.k \(\chi_{10470}(3277, \cdot)\) n/a 700 2
10470.2.m \(\chi_{10470}(1397, \cdot)\) n/a 1392 2
10470.2.o \(\chi_{10470}(2579, \cdot)\) n/a 1400 2
10470.2.q \(\chi_{10470}(911, \cdot)\) n/a 928 2
10470.2.s \(\chi_{10470}(2093, \cdot)\) n/a 1400 2
10470.2.u \(\chi_{10470}(1183, \cdot)\) n/a 700 2
10470.2.v \(\chi_{10470}(1519, \cdot)\) n/a 696 2
10470.2.y \(\chi_{10470}(7801, \cdot)\) n/a 464 2
10470.2.ba \(\chi_{10470}(8149, \cdot)\) n/a 704 2
10470.2.bc \(\chi_{10470}(373, \cdot)\) n/a 1400 4
10470.2.be \(\chi_{10470}(3263, \cdot)\) n/a 2800 4
10470.2.bg \(\chi_{10470}(509, \cdot)\) n/a 2800 4
10470.2.bi \(\chi_{10470}(1721, \cdot)\) n/a 1872 4
10470.2.bk \(\chi_{10470}(227, \cdot)\) n/a 2800 4
10470.2.bm \(\chi_{10470}(2467, \cdot)\) n/a 1400 4
10470.2.bo \(\chi_{10470}(31, \cdot)\) n/a 6608 28
10470.2.bq \(\chi_{10470}(139, \cdot)\) n/a 9744 28
10470.2.bs \(\chi_{10470}(289, \cdot)\) n/a 9856 28
10470.2.bu \(\chi_{10470}(121, \cdot)\) n/a 6608 28
10470.2.bw \(\chi_{10470}(151, \cdot)\) n/a 12992 56
10470.2.bx \(\chi_{10470}(103, \cdot)\) n/a 19600 56
10470.2.bz \(\chi_{10470}(17, \cdot)\) n/a 39200 56
10470.2.cb \(\chi_{10470}(11, \cdot)\) n/a 25984 56
10470.2.cd \(\chi_{10470}(179, \cdot)\) n/a 39200 56
10470.2.cf \(\chi_{10470}(257, \cdot)\) n/a 39200 56
10470.2.ch \(\chi_{10470}(133, \cdot)\) n/a 19600 56
10470.2.ck \(\chi_{10470}(19, \cdot)\) n/a 19712 56
10470.2.cm \(\chi_{10470}(91, \cdot)\) n/a 12992 56
10470.2.cp \(\chi_{10470}(49, \cdot)\) n/a 19488 56
10470.2.cr \(\chi_{10470}(13, \cdot)\) n/a 39200 112
10470.2.ct \(\chi_{10470}(83, \cdot)\) n/a 78400 112
10470.2.cv \(\chi_{10470}(71, \cdot)\) n/a 52416 112
10470.2.cx \(\chi_{10470}(59, \cdot)\) n/a 78400 112
10470.2.cz \(\chi_{10470}(23, \cdot)\) n/a 78400 112
10470.2.db \(\chi_{10470}(7, \cdot)\) n/a 39200 112

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(10470))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(10470)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(349))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(698))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1047))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1745))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2094))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3490))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5235))\)\(^{\oplus 2}\)