Properties

Label 2004.2
Level 2004
Weight 2
Dimension 48472
Nonzero newspaces 8
Sturm bound 446208
Trace bound 1

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Defining parameters

Level: \( N \) = \( 2004 = 2^{2} \cdot 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(446208\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2004))\).

Total New Old
Modular forms 113212 49128 64084
Cusp forms 109893 48472 61421
Eisenstein series 3319 656 2663

Trace form

\(48472q \) \(\mathstrut -\mathstrut 166q^{4} \) \(\mathstrut -\mathstrut 83q^{6} \) \(\mathstrut -\mathstrut 166q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(48472q \) \(\mathstrut -\mathstrut 166q^{4} \) \(\mathstrut -\mathstrut 83q^{6} \) \(\mathstrut -\mathstrut 166q^{9} \) \(\mathstrut -\mathstrut 166q^{10} \) \(\mathstrut -\mathstrut 83q^{12} \) \(\mathstrut -\mathstrut 332q^{13} \) \(\mathstrut -\mathstrut 166q^{16} \) \(\mathstrut -\mathstrut 83q^{18} \) \(\mathstrut -\mathstrut 166q^{21} \) \(\mathstrut -\mathstrut 166q^{22} \) \(\mathstrut -\mathstrut 83q^{24} \) \(\mathstrut -\mathstrut 332q^{25} \) \(\mathstrut -\mathstrut 166q^{28} \) \(\mathstrut -\mathstrut 83q^{30} \) \(\mathstrut -\mathstrut 166q^{33} \) \(\mathstrut -\mathstrut 166q^{34} \) \(\mathstrut -\mathstrut 83q^{36} \) \(\mathstrut -\mathstrut 332q^{37} \) \(\mathstrut -\mathstrut 166q^{40} \) \(\mathstrut -\mathstrut 83q^{42} \) \(\mathstrut -\mathstrut 166q^{45} \) \(\mathstrut -\mathstrut 166q^{46} \) \(\mathstrut -\mathstrut 83q^{48} \) \(\mathstrut -\mathstrut 332q^{49} \) \(\mathstrut -\mathstrut 166q^{52} \) \(\mathstrut -\mathstrut 83q^{54} \) \(\mathstrut -\mathstrut 166q^{57} \) \(\mathstrut -\mathstrut 166q^{58} \) \(\mathstrut -\mathstrut 83q^{60} \) \(\mathstrut -\mathstrut 332q^{61} \) \(\mathstrut -\mathstrut 166q^{64} \) \(\mathstrut -\mathstrut 83q^{66} \) \(\mathstrut -\mathstrut 166q^{69} \) \(\mathstrut -\mathstrut 166q^{70} \) \(\mathstrut -\mathstrut 83q^{72} \) \(\mathstrut -\mathstrut 332q^{73} \) \(\mathstrut -\mathstrut 166q^{76} \) \(\mathstrut -\mathstrut 83q^{78} \) \(\mathstrut -\mathstrut 166q^{81} \) \(\mathstrut -\mathstrut 166q^{82} \) \(\mathstrut -\mathstrut 83q^{84} \) \(\mathstrut -\mathstrut 332q^{85} \) \(\mathstrut -\mathstrut 166q^{88} \) \(\mathstrut -\mathstrut 83q^{90} \) \(\mathstrut -\mathstrut 166q^{93} \) \(\mathstrut -\mathstrut 166q^{94} \) \(\mathstrut -\mathstrut 83q^{96} \) \(\mathstrut -\mathstrut 332q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2004))\)

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
2004.2.a \(\chi_{2004}(1, \cdot)\) 2004.2.a.a 5 1
2004.2.a.b 5
2004.2.a.c 9
2004.2.a.d 9
2004.2.b \(\chi_{2004}(667, \cdot)\) n/a 168 1
2004.2.c \(\chi_{2004}(335, \cdot)\) n/a 332 1
2004.2.h \(\chi_{2004}(1001, \cdot)\) 2004.2.h.a 56 1
2004.2.i \(\chi_{2004}(25, \cdot)\) n/a 2296 82
2004.2.j \(\chi_{2004}(5, \cdot)\) n/a 4592 82
2004.2.o \(\chi_{2004}(11, \cdot)\) n/a 27224 82
2004.2.p \(\chi_{2004}(43, \cdot)\) n/a 13776 82

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2004))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2004)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(167))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(334))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(501))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(668))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1002))\)\(^{\oplus 2}\)