Properties

Label 4028.2
Level 4028
Weight 2
Dimension 291260
Nonzero newspaces 36
Sturm bound 2021760

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Defining parameters

Level: \( N \) = \( 4028 = 2^{2} \cdot 19 \cdot 53 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(2021760\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4028))\).

Total New Old
Modular forms 510120 294724 215396
Cusp forms 500761 291260 209501
Eisenstein series 9359 3464 5895

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4028))\)

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
4028.2.a \(\chi_{4028}(1, \cdot)\) 4028.2.a.a 1 1
4028.2.a.b 1
4028.2.a.c 19
4028.2.a.d 19
4028.2.a.e 19
4028.2.a.f 19
4028.2.b \(\chi_{4028}(4027, \cdot)\) n/a 536 1
4028.2.c \(\chi_{4028}(3497, \cdot)\) 4028.2.c.a 82 1
4028.2.h \(\chi_{4028}(531, \cdot)\) n/a 520 1
4028.2.i \(\chi_{4028}(425, \cdot)\) n/a 176 2
4028.2.j \(\chi_{4028}(189, \cdot)\) n/a 180 2
4028.2.m \(\chi_{4028}(3687, \cdot)\) n/a 972 2
4028.2.n \(\chi_{4028}(107, \cdot)\) n/a 1040 2
4028.2.s \(\chi_{4028}(635, \cdot)\) n/a 1072 2
4028.2.t \(\chi_{4028}(2861, \cdot)\) n/a 180 2
4028.2.u \(\chi_{4028}(213, \cdot)\) n/a 516 6
4028.2.w \(\chi_{4028}(825, \cdot)\) n/a 360 4
4028.2.x \(\chi_{4028}(83, \cdot)\) n/a 2144 4
4028.2.z \(\chi_{4028}(77, \cdot)\) n/a 960 12
4028.2.bc \(\chi_{4028}(529, \cdot)\) n/a 540 6
4028.2.bd \(\chi_{4028}(319, \cdot)\) n/a 3120 6
4028.2.bf \(\chi_{4028}(211, \cdot)\) n/a 3216 6
4028.2.bh \(\chi_{4028}(227, \cdot)\) n/a 6432 12
4028.2.bm \(\chi_{4028}(229, \cdot)\) n/a 984 12
4028.2.bn \(\chi_{4028}(303, \cdot)\) n/a 6432 12
4028.2.bo \(\chi_{4028}(23, \cdot)\) n/a 6432 12
4028.2.br \(\chi_{4028}(129, \cdot)\) n/a 1080 12
4028.2.bs \(\chi_{4028}(49, \cdot)\) n/a 2160 24
4028.2.bt \(\chi_{4028}(39, \cdot)\) n/a 11664 24
4028.2.bw \(\chi_{4028}(569, \cdot)\) n/a 2160 24
4028.2.bx \(\chi_{4028}(197, \cdot)\) n/a 2160 24
4028.2.by \(\chi_{4028}(255, \cdot)\) n/a 12864 24
4028.2.cd \(\chi_{4028}(183, \cdot)\) n/a 12864 24
4028.2.ce \(\chi_{4028}(81, \cdot)\) n/a 6480 72
4028.2.cg \(\chi_{4028}(87, \cdot)\) n/a 25728 48
4028.2.ch \(\chi_{4028}(65, \cdot)\) n/a 4320 48
4028.2.ck \(\chi_{4028}(59, \cdot)\) n/a 38592 72
4028.2.cm \(\chi_{4028}(15, \cdot)\) n/a 38592 72
4028.2.cn \(\chi_{4028}(9, \cdot)\) n/a 6480 72
4028.2.cq \(\chi_{4028}(21, \cdot)\) n/a 12960 144
4028.2.ct \(\chi_{4028}(35, \cdot)\) n/a 77184 144

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4028))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4028)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(53))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(106))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(212))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1007))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2014))\)\(^{\oplus 2}\)