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Properties

Label 2007.2
Level 2007
Weight 2
Dimension 117105
Nonzero newspaces 20
Sturm bound 596736
Trace bound 5

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Defining parameters

Level: \( N \) = \( 2007 = 3^{2} \cdot 223 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(596736\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2007))\).

Total New Old
Modular forms 150960 119093 31867
Cusp forms 147409 117105 30304
Eisenstein series 3551 1988 1563

Trace form

\( 117105 q - 333 q^{2} - 444 q^{3} - 333 q^{4} - 333 q^{5} - 444 q^{6} - 333 q^{7} - 333 q^{8} - 444 q^{9} + O(q^{10}) \) \( 117105 q - 333 q^{2} - 444 q^{3} - 333 q^{4} - 333 q^{5} - 444 q^{6} - 333 q^{7} - 333 q^{8} - 444 q^{9} - 999 q^{10} - 333 q^{11} - 444 q^{12} - 333 q^{13} - 333 q^{14} - 444 q^{15} - 333 q^{16} - 333 q^{17} - 444 q^{18} - 999 q^{19} - 333 q^{20} - 444 q^{21} - 333 q^{22} - 333 q^{23} - 444 q^{24} - 333 q^{25} - 333 q^{26} - 444 q^{27} - 999 q^{28} - 333 q^{29} - 444 q^{30} - 333 q^{31} - 333 q^{32} - 444 q^{33} - 333 q^{34} - 333 q^{35} - 444 q^{36} - 999 q^{37} - 333 q^{38} - 444 q^{39} - 333 q^{40} - 333 q^{41} - 444 q^{42} - 333 q^{43} - 333 q^{44} - 444 q^{45} - 999 q^{46} - 333 q^{47} - 444 q^{48} - 333 q^{49} - 333 q^{50} - 444 q^{51} - 333 q^{52} - 333 q^{53} - 444 q^{54} - 999 q^{55} - 333 q^{56} - 444 q^{57} - 333 q^{58} - 333 q^{59} - 444 q^{60} - 333 q^{61} - 333 q^{62} - 444 q^{63} - 999 q^{64} - 333 q^{65} - 444 q^{66} - 333 q^{67} - 333 q^{68} - 444 q^{69} - 333 q^{70} - 333 q^{71} - 444 q^{72} - 999 q^{73} - 333 q^{74} - 444 q^{75} - 333 q^{76} - 333 q^{77} - 444 q^{78} - 333 q^{79} - 333 q^{80} - 444 q^{81} - 999 q^{82} - 333 q^{83} - 444 q^{84} - 333 q^{85} - 333 q^{86} - 444 q^{87} - 333 q^{88} - 333 q^{89} - 444 q^{90} - 999 q^{91} - 333 q^{92} - 444 q^{93} - 333 q^{94} - 333 q^{95} - 444 q^{96} - 333 q^{97} - 333 q^{98} - 444 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2007))\)

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
2007.2.a \(\chi_{2007}(1, \cdot)\) 2007.2.a.a 1 1
2007.2.a.b 2
2007.2.a.c 2
2007.2.a.d 2
2007.2.a.e 2
2007.2.a.f 3
2007.2.a.g 3
2007.2.a.h 3
2007.2.a.i 4
2007.2.a.j 6
2007.2.a.k 6
2007.2.a.l 7
2007.2.a.m 12
2007.2.a.n 14
2007.2.a.o 26
2007.2.c \(\chi_{2007}(2006, \cdot)\) 2007.2.c.a 28 1
2007.2.c.b 48
2007.2.e \(\chi_{2007}(1075, \cdot)\) n/a 444 2
2007.2.f \(\chi_{2007}(670, \cdot)\) n/a 444 2
2007.2.g \(\chi_{2007}(931, \cdot)\) n/a 444 2
2007.2.h \(\chi_{2007}(262, \cdot)\) n/a 184 2
2007.2.i \(\chi_{2007}(1601, \cdot)\) n/a 148 2
2007.2.o \(\chi_{2007}(668, \cdot)\) n/a 444 2
2007.2.p \(\chi_{2007}(407, \cdot)\) n/a 444 2
2007.2.s \(\chi_{2007}(263, \cdot)\) n/a 444 2
2007.2.u \(\chi_{2007}(28, \cdot)\) n/a 3348 36
2007.2.w \(\chi_{2007}(26, \cdot)\) n/a 2736 36
2007.2.y \(\chi_{2007}(19, \cdot)\) n/a 6624 72
2007.2.z \(\chi_{2007}(31, \cdot)\) n/a 15984 72
2007.2.ba \(\chi_{2007}(4, \cdot)\) n/a 15984 72
2007.2.bb \(\chi_{2007}(25, \cdot)\) n/a 15984 72
2007.2.bd \(\chi_{2007}(11, \cdot)\) n/a 15984 72
2007.2.bg \(\chi_{2007}(5, \cdot)\) n/a 15984 72
2007.2.bh \(\chi_{2007}(59, \cdot)\) n/a 15984 72
2007.2.bn \(\chi_{2007}(35, \cdot)\) n/a 5328 72

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2007))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2007)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(223))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(669))\)\(^{\oplus 2}\)