Properties

Label 4031.2
Level 4031
Weight 2
Dimension 670819
Nonzero newspaces 24
Sturm bound 2704800

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Defining parameters

Level: \( N \) = \( 4031 = 29 \cdot 139 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(2704800\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4031))\).

Total New Old
Modular forms 680064 678219 1845
Cusp forms 672337 670819 1518
Eisenstein series 7727 7400 327

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4031))\)

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
4031.2.a \(\chi_{4031}(1, \cdot)\) 4031.2.a.a 2 1
4031.2.a.b 59
4031.2.a.c 61
4031.2.a.d 98
4031.2.a.e 103
4031.2.b \(\chi_{4031}(1391, \cdot)\) n/a 344 1
4031.2.e \(\chi_{4031}(320, \cdot)\) n/a 652 2
4031.2.g \(\chi_{4031}(3057, \cdot)\) n/a 696 2
4031.2.j \(\chi_{4031}(1710, \cdot)\) n/a 696 2
4031.2.k \(\chi_{4031}(140, \cdot)\) n/a 2076 6
4031.2.l \(\chi_{4031}(1433, \cdot)\) n/a 1392 4
4031.2.p \(\chi_{4031}(557, \cdot)\) n/a 2064 6
4031.2.q \(\chi_{4031}(181, \cdot)\) n/a 4176 12
4031.2.r \(\chi_{4031}(175, \cdot)\) n/a 7216 22
4031.2.s \(\chi_{4031}(416, \cdot)\) n/a 4176 12
4031.2.u \(\chi_{4031}(42, \cdot)\) n/a 4176 12
4031.2.z \(\chi_{4031}(57, \cdot)\) n/a 7656 22
4031.2.ba \(\chi_{4031}(30, \cdot)\) n/a 14344 44
4031.2.bc \(\chi_{4031}(43, \cdot)\) n/a 8352 24
4031.2.bd \(\chi_{4031}(75, \cdot)\) n/a 15312 44
4031.2.bf \(\chi_{4031}(28, \cdot)\) n/a 15312 44
4031.2.bi \(\chi_{4031}(36, \cdot)\) n/a 45936 132
4031.2.bk \(\chi_{4031}(12, \cdot)\) n/a 30624 88
4031.2.bl \(\chi_{4031}(6, \cdot)\) n/a 45936 132
4031.2.bo \(\chi_{4031}(7, \cdot)\) n/a 91872 264
4031.2.bq \(\chi_{4031}(8, \cdot)\) n/a 91872 264
4031.2.bt \(\chi_{4031}(4, \cdot)\) n/a 91872 264
4031.2.bu \(\chi_{4031}(2, \cdot)\) n/a 183744 528

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4031))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4031)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(139))\)\(^{\oplus 2}\)