Properties

Label 2002.2.a
Level 2002
Weight 2
Character orbit a
Rep. character \(\chi_{2002}(1,\cdot)\)
Character field \(\Q\)
Dimension 61
Newforms 19
Sturm bound 672
Trace bound 9

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Defining parameters

Level: \( N \) = \( 2002 = 2 \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 2002.a (trivial)
Character field: \(\Q\)
Newforms: \( 19 \)
Sturm bound: \(672\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\), \(5\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2002))\).

Total New Old
Modular forms 344 61 283
Cusp forms 329 61 268
Eisenstein series 15 0 15

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(7\)\(11\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(5\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(4\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(2\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(4\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(4\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(5\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(5\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(2\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(6\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(3\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(6\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(5\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(27\)
Minus space\(-\)\(34\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2002))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7 11 13
2002.2.a.a \(1\) \(15.986\) \(\Q\) None \(-1\) \(0\) \(2\) \(-1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+2q^{5}-q^{7}-q^{8}-3q^{9}+\cdots\)
2002.2.a.b \(1\) \(15.986\) \(\Q\) None \(-1\) \(0\) \(2\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-3q^{9}+\cdots\)
2002.2.a.c \(1\) \(15.986\) \(\Q\) None \(1\) \(0\) \(4\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+4q^{5}+q^{7}+q^{8}-3q^{9}+\cdots\)
2002.2.a.d \(2\) \(15.986\) \(\Q(\sqrt{5}) \) None \(-2\) \(-1\) \(-1\) \(-2\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-\beta q^{3}+q^{4}+(-1+\beta )q^{5}+\beta q^{6}+\cdots\)
2002.2.a.e \(2\) \(15.986\) \(\Q(\sqrt{13}) \) None \(-2\) \(1\) \(-1\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+\beta q^{3}+q^{4}+(-1+\beta )q^{5}-\beta q^{6}+\cdots\)
2002.2.a.f \(2\) \(15.986\) \(\Q(\sqrt{5}) \) None \(2\) \(-3\) \(-5\) \(2\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+(-1-\beta )q^{3}+q^{4}+(-2-\beta )q^{5}+\cdots\)
2002.2.a.g \(2\) \(15.986\) \(\Q(\sqrt{5}) \) None \(2\) \(-1\) \(-1\) \(-2\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-\beta q^{3}+q^{4}+(-1+\beta )q^{5}-\beta q^{6}+\cdots\)
2002.2.a.h \(2\) \(15.986\) \(\Q(\sqrt{13}) \) None \(2\) \(-1\) \(-1\) \(-2\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-\beta q^{3}+q^{4}+(-1+\beta )q^{5}-\beta q^{6}+\cdots\)
2002.2.a.i \(3\) \(15.986\) 3.3.469.1 None \(-3\) \(1\) \(5\) \(3\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(2+\beta _{2})q^{5}-\beta _{1}q^{6}+\cdots\)
2002.2.a.j \(3\) \(15.986\) 3.3.733.1 None \(-3\) \(3\) \(-1\) \(-3\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+(1+\beta _{2})q^{3}+q^{4}-\beta _{1}q^{5}+(-1+\cdots)q^{6}+\cdots\)
2002.2.a.k \(3\) \(15.986\) 3.3.229.1 None \(3\) \(-3\) \(-5\) \(3\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-2-\beta _{2})q^{5}+\cdots\)
2002.2.a.l \(4\) \(15.986\) 4.4.14272.1 None \(-4\) \(-2\) \(-2\) \(-4\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1-\beta _{3})q^{5}+\cdots\)
2002.2.a.m \(4\) \(15.986\) \(\Q(\sqrt{2}, \sqrt{5})\) None \(-4\) \(-2\) \(-2\) \(4\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+(-1-\beta _{2})q^{3}+q^{4}+(-1+\beta _{3})q^{5}+\cdots\)
2002.2.a.n \(5\) \(15.986\) 5.5.2055632.1 None \(-5\) \(-2\) \(-6\) \(5\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(-2+\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
2002.2.a.o \(5\) \(15.986\) 5.5.4179152.1 None \(-5\) \(-2\) \(0\) \(-5\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{3}q^{5}+\beta _{1}q^{6}+\cdots\)
2002.2.a.p \(5\) \(15.986\) 5.5.9353072.1 None \(5\) \(0\) \(4\) \(-5\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(1+\beta _{2})q^{5}+\beta _{1}q^{6}+\cdots\)
2002.2.a.q \(5\) \(15.986\) 5.5.3430384.1 None \(5\) \(4\) \(2\) \(5\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+(1-\beta _{4})q^{3}+q^{4}+\beta _{1}q^{5}+(1+\cdots)q^{6}+\cdots\)
2002.2.a.r \(5\) \(15.986\) 5.5.1590832.1 None \(5\) \(4\) \(4\) \(5\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1+\beta _{3})q^{5}+\cdots\)
2002.2.a.s \(6\) \(15.986\) 6.6.1385718192.1 None \(6\) \(0\) \(0\) \(-6\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{4}q^{5}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2002))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2002)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(286))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1001))\)\(^{\oplus 2}\)