Properties

Label 4508.2
Level 4508
Weight 2
Dimension 344224
Nonzero newspaces 32
Sturm bound 2483712

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Defining parameters

Level: \( N \) = \( 4508 = 2^{2} \cdot 7^{2} \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(2483712\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4508))\).

Total New Old
Modular forms 627528 348300 279228
Cusp forms 614329 344224 270105
Eisenstein series 13199 4076 9123

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4508))\)

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
4508.2.a \(\chi_{4508}(1, \cdot)\) 4508.2.a.a 1 1
4508.2.a.b 1
4508.2.a.c 1
4508.2.a.d 1
4508.2.a.e 4
4508.2.a.f 5
4508.2.a.g 5
4508.2.a.h 6
4508.2.a.i 6
4508.2.a.j 6
4508.2.a.k 7
4508.2.a.l 7
4508.2.a.m 7
4508.2.a.n 7
4508.2.a.o 10
4508.2.c \(\chi_{4508}(1471, \cdot)\) n/a 482 1
4508.2.d \(\chi_{4508}(2253, \cdot)\) 4508.2.d.a 32 1
4508.2.d.b 48
4508.2.f \(\chi_{4508}(783, \cdot)\) n/a 440 1
4508.2.i \(\chi_{4508}(3313, \cdot)\) n/a 148 2
4508.2.k \(\chi_{4508}(1795, \cdot)\) n/a 880 2
4508.2.m \(\chi_{4508}(3265, \cdot)\) n/a 160 2
4508.2.p \(\chi_{4508}(275, \cdot)\) n/a 944 2
4508.2.q \(\chi_{4508}(645, \cdot)\) n/a 624 6
4508.2.r \(\chi_{4508}(197, \cdot)\) n/a 820 10
4508.2.u \(\chi_{4508}(139, \cdot)\) n/a 3696 6
4508.2.w \(\chi_{4508}(321, \cdot)\) n/a 672 6
4508.2.x \(\chi_{4508}(183, \cdot)\) n/a 4008 6
4508.2.z \(\chi_{4508}(93, \cdot)\) n/a 1224 12
4508.2.bc \(\chi_{4508}(587, \cdot)\) n/a 4720 10
4508.2.be \(\chi_{4508}(97, \cdot)\) n/a 800 10
4508.2.bf \(\chi_{4508}(99, \cdot)\) n/a 4820 10
4508.2.bh \(\chi_{4508}(165, \cdot)\) n/a 1600 20
4508.2.bi \(\chi_{4508}(919, \cdot)\) n/a 8016 12
4508.2.bl \(\chi_{4508}(45, \cdot)\) n/a 1344 12
4508.2.bn \(\chi_{4508}(47, \cdot)\) n/a 7392 12
4508.2.bp \(\chi_{4508}(67, \cdot)\) n/a 9440 20
4508.2.bs \(\chi_{4508}(129, \cdot)\) n/a 1600 20
4508.2.bu \(\chi_{4508}(31, \cdot)\) n/a 9440 20
4508.2.bw \(\chi_{4508}(29, \cdot)\) n/a 6720 60
4508.2.by \(\chi_{4508}(15, \cdot)\) n/a 40080 60
4508.2.bz \(\chi_{4508}(125, \cdot)\) n/a 6720 60
4508.2.cb \(\chi_{4508}(27, \cdot)\) n/a 40080 60
4508.2.ce \(\chi_{4508}(9, \cdot)\) n/a 13440 120
4508.2.cg \(\chi_{4508}(3, \cdot)\) n/a 80160 120
4508.2.ci \(\chi_{4508}(5, \cdot)\) n/a 13440 120
4508.2.cl \(\chi_{4508}(11, \cdot)\) n/a 80160 120

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4508))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4508)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(322))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(644))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1127))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2254))\)\(^{\oplus 2}\)