Properties

Label 2254.4
Level 2254
Weight 4
Dimension 148398
Nonzero newspaces 16
Sturm bound 1241856
Trace bound 5

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Defining parameters

Level: \( N \) = \( 2254 = 2 \cdot 7^{2} \cdot 23 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(1241856\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2254))\).

Total New Old
Modular forms 468336 148398 319938
Cusp forms 463056 148398 314658
Eisenstein series 5280 0 5280

Trace form

\( 148398 q + 48 q^{3} - 96 q^{5} - 144 q^{6} - 96 q^{7} + 168 q^{9} + 144 q^{10} + 168 q^{11} + 192 q^{12} + 264 q^{13} + 264 q^{14} + 700 q^{15} - 424 q^{17} - 760 q^{18} - 460 q^{19} - 832 q^{20} - 144 q^{21}+ \cdots + 28542 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2254))\)

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
2254.4.a \(\chi_{2254}(1, \cdot)\) 2254.4.a.a 1 1
2254.4.a.b 1
2254.4.a.c 2
2254.4.a.d 2
2254.4.a.e 2
2254.4.a.f 2
2254.4.a.g 2
2254.4.a.h 3
2254.4.a.i 3
2254.4.a.j 4
2254.4.a.k 5
2254.4.a.l 5
2254.4.a.m 6
2254.4.a.n 6
2254.4.a.o 8
2254.4.a.p 8
2254.4.a.q 10
2254.4.a.r 11
2254.4.a.s 11
2254.4.a.t 11
2254.4.a.u 11
2254.4.a.v 11
2254.4.a.w 11
2254.4.a.x 11
2254.4.a.y 11
2254.4.a.z 14
2254.4.a.ba 16
2254.4.a.bb 18
2254.4.a.bc 20
2254.4.c \(\chi_{2254}(2253, \cdot)\) n/a 240 1
2254.4.e \(\chi_{2254}(1059, \cdot)\) n/a 440 2
2254.4.g \(\chi_{2254}(1011, \cdot)\) n/a 480 2
2254.4.i \(\chi_{2254}(323, \cdot)\) n/a 1848 6
2254.4.j \(\chi_{2254}(197, \cdot)\) n/a 2460 10
2254.4.l \(\chi_{2254}(321, \cdot)\) n/a 2016 6
2254.4.n \(\chi_{2254}(93, \cdot)\) n/a 3696 12
2254.4.p \(\chi_{2254}(97, \cdot)\) n/a 2400 10
2254.4.r \(\chi_{2254}(165, \cdot)\) n/a 4800 20
2254.4.t \(\chi_{2254}(45, \cdot)\) n/a 4032 12
2254.4.w \(\chi_{2254}(19, \cdot)\) n/a 4800 20
2254.4.y \(\chi_{2254}(29, \cdot)\) n/a 20160 60
2254.4.ba \(\chi_{2254}(83, \cdot)\) n/a 20160 60
2254.4.bc \(\chi_{2254}(9, \cdot)\) n/a 40320 120
2254.4.be \(\chi_{2254}(5, \cdot)\) n/a 40320 120

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2254))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2254)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(322))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1127))\)\(^{\oplus 2}\)