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Properties

Label 615.4
Level 615
Weight 4
Dimension 27452
Nonzero newspaces 28
Sturm bound 107520
Trace bound 9

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Defining parameters

Level: \( N \) = \( 615 = 3 \cdot 5 \cdot 41 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 28 \)
Sturm bound: \(107520\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(615))\).

Total New Old
Modular forms 40960 27916 13044
Cusp forms 39680 27452 12228
Eisenstein series 1280 464 816

Trace form

\( 27452 q - 8 q^{2} - 28 q^{3} - 32 q^{4} - 12 q^{5} - 120 q^{6} - 40 q^{7} + 72 q^{8} - 4 q^{9} + 72 q^{10} + 112 q^{11} - 256 q^{12} - 408 q^{13} - 528 q^{14} - 408 q^{15} - 848 q^{16} - 80 q^{17} + 368 q^{18}+ \cdots - 2056 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(615))\)

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
615.4.a \(\chi_{615}(1, \cdot)\) 615.4.a.a 1 1
615.4.a.b 1
615.4.a.c 1
615.4.a.d 2
615.4.a.e 8
615.4.a.f 8
615.4.a.g 9
615.4.a.h 10
615.4.a.i 13
615.4.a.j 13
615.4.a.k 14
615.4.b \(\chi_{615}(124, \cdot)\) n/a 120 1
615.4.e \(\chi_{615}(409, \cdot)\) n/a 128 1
615.4.f \(\chi_{615}(286, \cdot)\) 615.4.f.a 42 1
615.4.f.b 42
615.4.j \(\chi_{615}(91, \cdot)\) n/a 168 2
615.4.k \(\chi_{615}(278, \cdot)\) n/a 496 2
615.4.m \(\chi_{615}(83, \cdot)\) n/a 480 2
615.4.p \(\chi_{615}(122, \cdot)\) n/a 496 2
615.4.r \(\chi_{615}(32, \cdot)\) n/a 496 2
615.4.s \(\chi_{615}(214, \cdot)\) n/a 248 2
615.4.u \(\chi_{615}(16, \cdot)\) n/a 336 4
615.4.w \(\chi_{615}(208, \cdot)\) n/a 504 4
615.4.x \(\chi_{615}(14, \cdot)\) n/a 992 4
615.4.ba \(\chi_{615}(161, \cdot)\) n/a 672 4
615.4.bb \(\chi_{615}(178, \cdot)\) n/a 504 4
615.4.bf \(\chi_{615}(31, \cdot)\) n/a 336 4
615.4.bg \(\chi_{615}(4, \cdot)\) n/a 512 4
615.4.bj \(\chi_{615}(139, \cdot)\) n/a 512 4
615.4.bl \(\chi_{615}(49, \cdot)\) n/a 992 8
615.4.bm \(\chi_{615}(2, \cdot)\) n/a 1984 8
615.4.bo \(\chi_{615}(23, \cdot)\) n/a 1984 8
615.4.br \(\chi_{615}(92, \cdot)\) n/a 1984 8
615.4.bt \(\chi_{615}(62, \cdot)\) n/a 1984 8
615.4.bu \(\chi_{615}(46, \cdot)\) n/a 672 8
615.4.bx \(\chi_{615}(7, \cdot)\) n/a 2016 16
615.4.by \(\chi_{615}(11, \cdot)\) n/a 2688 16
615.4.cb \(\chi_{615}(29, \cdot)\) n/a 3968 16
615.4.cc \(\chi_{615}(13, \cdot)\) n/a 2016 16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(615))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(615)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(123))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(205))\)\(^{\oplus 2}\)