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Properties

Label 4074.2
Level 4074
Weight 2
Dimension 108165
Nonzero newspaces 60
Sturm bound 1806336

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Defining parameters

Level: \( N \) = \( 4074 = 2 \cdot 3 \cdot 7 \cdot 97 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(1806336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4074))\).

Total New Old
Modular forms 456192 108165 348027
Cusp forms 446977 108165 338812
Eisenstein series 9215 0 9215

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4074))\)

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
4074.2.a \(\chi_{4074}(1, \cdot)\) 4074.2.a.a 1 1
4074.2.a.b 1
4074.2.a.c 1
4074.2.a.d 1
4074.2.a.e 1
4074.2.a.f 1
4074.2.a.g 1
4074.2.a.h 1
4074.2.a.i 1
4074.2.a.j 1
4074.2.a.k 1
4074.2.a.l 1
4074.2.a.m 1
4074.2.a.n 2
4074.2.a.o 2
4074.2.a.p 2
4074.2.a.q 2
4074.2.a.r 3
4074.2.a.s 3
4074.2.a.t 3
4074.2.a.u 3
4074.2.a.v 4
4074.2.a.w 4
4074.2.a.x 4
4074.2.a.y 5
4074.2.a.z 6
4074.2.a.ba 6
4074.2.a.bb 6
4074.2.a.bc 6
4074.2.a.bd 6
4074.2.a.be 7
4074.2.a.bf 10
4074.2.c \(\chi_{4074}(4073, \cdot)\) n/a 264 1
4074.2.d \(\chi_{4074}(2521, \cdot)\) 4074.2.d.a 2 1
4074.2.d.b 24
4074.2.d.c 24
4074.2.d.d 24
4074.2.d.e 26
4074.2.f \(\chi_{4074}(1553, \cdot)\) n/a 256 1
4074.2.i \(\chi_{4074}(2389, \cdot)\) n/a 260 2
4074.2.j \(\chi_{4074}(1807, \cdot)\) n/a 200 2
4074.2.k \(\chi_{4074}(583, \cdot)\) n/a 256 2
4074.2.l \(\chi_{4074}(2557, \cdot)\) n/a 260 2
4074.2.m \(\chi_{4074}(463, \cdot)\) n/a 200 2
4074.2.p \(\chi_{4074}(2015, \cdot)\) n/a 528 2
4074.2.q \(\chi_{4074}(521, \cdot)\) n/a 524 2
4074.2.t \(\chi_{4074}(1129, \cdot)\) n/a 260 2
4074.2.y \(\chi_{4074}(971, \cdot)\) n/a 512 2
4074.2.ba \(\chi_{4074}(3359, \cdot)\) n/a 520 2
4074.2.bb \(\chi_{4074}(1781, \cdot)\) n/a 524 2
4074.2.be \(\chi_{4074}(193, \cdot)\) n/a 264 2
4074.2.bg \(\chi_{4074}(547, \cdot)\) n/a 200 2
4074.2.bh \(\chi_{4074}(1297, \cdot)\) n/a 260 2
4074.2.bk \(\chi_{4074}(353, \cdot)\) n/a 524 2
4074.2.bl \(\chi_{4074}(2099, \cdot)\) n/a 520 2
4074.2.bn \(\chi_{4074}(2327, \cdot)\) n/a 520 2
4074.2.bq \(\chi_{4074}(1613, \cdot)\) n/a 524 2
4074.2.bs \(\chi_{4074}(629, \cdot)\) n/a 1056 4
4074.2.bt \(\chi_{4074}(421, \cdot)\) n/a 400 4
4074.2.bx \(\chi_{4074}(1255, \cdot)\) n/a 520 4
4074.2.bz \(\chi_{4074}(2225, \cdot)\) n/a 1040 4
4074.2.ca \(\chi_{4074}(269, \cdot)\) n/a 1040 4
4074.2.cd \(\chi_{4074}(479, \cdot)\) n/a 1048 4
4074.2.ce \(\chi_{4074}(1633, \cdot)\) n/a 520 4
4074.2.ch \(\chi_{4074}(673, \cdot)\) n/a 400 4
4074.2.ci \(\chi_{4074}(1045, \cdot)\) n/a 528 4
4074.2.ck \(\chi_{4074}(857, \cdot)\) n/a 1048 4
4074.2.cn \(\chi_{4074}(167, \cdot)\) n/a 2112 8
4074.2.co \(\chi_{4074}(85, \cdot)\) n/a 768 8
4074.2.cs \(\chi_{4074}(823, \cdot)\) n/a 1056 8
4074.2.ct \(\chi_{4074}(47, \cdot)\) n/a 2080 8
4074.2.cu \(\chi_{4074}(43, \cdot)\) n/a 800 8
4074.2.cv \(\chi_{4074}(461, \cdot)\) n/a 2080 8
4074.2.da \(\chi_{4074}(1265, \cdot)\) n/a 2096 8
4074.2.db \(\chi_{4074}(121, \cdot)\) n/a 1040 8
4074.2.dc \(\chi_{4074}(101, \cdot)\) n/a 2096 8
4074.2.dd \(\chi_{4074}(151, \cdot)\) n/a 1040 8
4074.2.dh \(\chi_{4074}(55, \cdot)\) n/a 2048 16
4074.2.dj \(\chi_{4074}(239, \cdot)\) n/a 3136 16
4074.2.dk \(\chi_{4074}(593, \cdot)\) n/a 4192 16
4074.2.dn \(\chi_{4074}(25, \cdot)\) n/a 2080 16
4074.2.do \(\chi_{4074}(79, \cdot)\) n/a 2112 16
4074.2.dq \(\chi_{4074}(169, \cdot)\) n/a 1536 16
4074.2.dt \(\chi_{4074}(293, \cdot)\) n/a 4160 16
4074.2.dv \(\chi_{4074}(89, \cdot)\) n/a 4160 16
4074.2.dw \(\chi_{4074}(437, \cdot)\) n/a 4192 16
4074.2.dz \(\chi_{4074}(205, \cdot)\) n/a 2080 16
4074.2.eb \(\chi_{4074}(157, \cdot)\) n/a 4160 32
4074.2.ec \(\chi_{4074}(29, \cdot)\) n/a 6272 32
4074.2.ee \(\chi_{4074}(149, \cdot)\) n/a 8320 32
4074.2.eg \(\chi_{4074}(179, \cdot)\) n/a 8384 32
4074.2.ei \(\chi_{4074}(13, \cdot)\) n/a 4224 32
4074.2.ek \(\chi_{4074}(187, \cdot)\) n/a 4160 32
4074.2.em \(\chi_{4074}(19, \cdot)\) n/a 4224 32
4074.2.ep \(\chi_{4074}(23, \cdot)\) n/a 8384 32

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4074))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4074)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(97))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(194))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(291))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(582))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(679))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1358))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2037))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4074))\)\(^{\oplus 1}\)