Properties

Label 4001.2
Level 4001
Weight 2
Dimension 665001
Nonzero newspaces 20
Sturm bound 2668000

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Defining parameters

Level: \( N \) = \( 4001 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(2668000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4001))\).

Total New Old
Modular forms 669000 669000 0
Cusp forms 665001 665001 0
Eisenstein series 3999 3999 0

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4001))\)

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
4001.2.a \(\chi_{4001}(1, \cdot)\) 4001.2.a.a 149 1
4001.2.a.b 184
4001.2.b \(\chi_{4001}(4000, \cdot)\) n/a 332 1
4001.2.c \(\chi_{4001}(899, \cdot)\) n/a 664 2
4001.2.d \(\chi_{4001}(902, \cdot)\) n/a 1328 4
4001.2.e \(\chi_{4001}(70, \cdot)\) n/a 1328 4
4001.2.f \(\chi_{4001}(614, \cdot)\) n/a 1328 4
4001.2.g \(\chi_{4001}(1115, \cdot)\) n/a 2664 8
4001.2.h \(\chi_{4001}(152, \cdot)\) n/a 2656 8
4001.2.i \(\chi_{4001}(196, \cdot)\) n/a 6640 20
4001.2.k \(\chi_{4001}(673, \cdot)\) n/a 5312 16
4001.2.l \(\chi_{4001}(14, \cdot)\) n/a 6640 20
4001.2.m \(\chi_{4001}(121, \cdot)\) n/a 10656 32
4001.2.n \(\chi_{4001}(25, \cdot)\) n/a 13280 40
4001.2.o \(\chi_{4001}(26, \cdot)\) n/a 33200 100
4001.2.q \(\chi_{4001}(5, \cdot)\) n/a 26560 80
4001.2.r \(\chi_{4001}(16, \cdot)\) n/a 33200 100
4001.2.s \(\chi_{4001}(58, \cdot)\) n/a 53280 160
4001.2.t \(\chi_{4001}(4, \cdot)\) n/a 66400 200
4001.2.v \(\chi_{4001}(2, \cdot)\) n/a 132800 400
4001.2.w \(\chi_{4001}(9, \cdot)\) n/a 266400 800

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