Properties

Label 2001.2.a
Level $2001$
Weight $2$
Character orbit 2001.a
Rep. character $\chi_{2001}(1,\cdot)$
Character field $\Q$
Dimension $103$
Newform subspaces $15$
Sturm bound $480$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 2001 = 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2001.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 15 \)
Sturm bound: \(480\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2001))\).

Total New Old
Modular forms 244 103 141
Cusp forms 237 103 134
Eisenstein series 7 0 7

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

\(3\)\(23\)\(29\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(14\)
\(+\)\(+\)\(-\)\(-\)\(13\)
\(+\)\(-\)\(+\)\(-\)\(14\)
\(+\)\(-\)\(-\)\(+\)\(9\)
\(-\)\(+\)\(+\)\(-\)\(16\)
\(-\)\(+\)\(-\)\(+\)\(9\)
\(-\)\(-\)\(+\)\(+\)\(8\)
\(-\)\(-\)\(-\)\(-\)\(20\)
Plus space\(+\)\(40\)
Minus space\(-\)\(63\)

Trace form

\( 103q - 3q^{2} + 3q^{3} + 101q^{4} - 6q^{5} - 3q^{6} + 9q^{8} + 103q^{9} + O(q^{10}) \) \( 103q - 3q^{2} + 3q^{3} + 101q^{4} - 6q^{5} - 3q^{6} + 9q^{8} + 103q^{9} + 22q^{10} - 12q^{11} + 21q^{12} + 2q^{13} + 32q^{14} - 6q^{15} + 133q^{16} - 18q^{17} - 3q^{18} - 4q^{19} + 14q^{20} + 16q^{21} - 8q^{22} - q^{23} - 3q^{24} + 81q^{25} - 10q^{26} + 3q^{27} + 4q^{28} - q^{29} - 2q^{30} + 8q^{31} + 25q^{32} - 12q^{33} + 30q^{34} + 101q^{36} - 14q^{37} + 4q^{38} + 26q^{39} + 6q^{40} - 34q^{41} - 12q^{42} + 12q^{43} - 12q^{44} - 6q^{45} + 5q^{46} + 24q^{47} + 29q^{48} + 95q^{49} - 53q^{50} - 18q^{51} + 10q^{52} - 22q^{53} - 3q^{54} + 32q^{55} + 24q^{56} + 20q^{57} + q^{58} + 36q^{59} - 42q^{60} - 30q^{61} - 32q^{62} + 137q^{64} - 28q^{65} - 20q^{66} + 36q^{67} - 38q^{68} + 7q^{69} + 32q^{70} + 80q^{71} + 9q^{72} + 14q^{73} + 86q^{74} + 29q^{75} - 60q^{76} - 8q^{77} - 14q^{78} + 24q^{79} + 38q^{80} + 103q^{81} - 38q^{82} + 4q^{83} + 16q^{84} - 20q^{85} - 36q^{86} + 11q^{87} + 20q^{88} + 22q^{89} + 22q^{90} + 48q^{91} - 7q^{92} + 8q^{93} - 60q^{94} + 56q^{95} - 39q^{96} - 18q^{97} + 29q^{98} - 12q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2001))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 23 29
2001.2.a.a \(1\) \(15.978\) \(\Q\) None \(-1\) \(-1\) \(3\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}-q^{4}+3q^{5}+q^{6}+3q^{8}+\cdots\)
2001.2.a.b \(1\) \(15.978\) \(\Q\) None \(0\) \(-1\) \(4\) \(-4\) \(+\) \(-\) \(+\) \(q-q^{3}-2q^{4}+4q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots\)
2001.2.a.c \(1\) \(15.978\) \(\Q\) None \(0\) \(1\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+q^{3}-2q^{4}+q^{9}-4q^{11}-2q^{12}+\cdots\)
2001.2.a.d \(2\) \(15.978\) \(\Q(\sqrt{5}) \) None \(-2\) \(-2\) \(-4\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}+3q^{8}+\cdots\)
2001.2.a.e \(2\) \(15.978\) \(\Q(\sqrt{6}) \) None \(0\) \(2\) \(0\) \(-4\) \(-\) \(+\) \(-\) \(q+q^{3}-2q^{4}-\beta q^{5}+(-2+\beta )q^{7}+\cdots\)
2001.2.a.f \(2\) \(15.978\) \(\Q(\sqrt{17}) \) None \(2\) \(-2\) \(-3\) \(0\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}-q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
2001.2.a.g \(4\) \(15.978\) 4.4.5744.1 None \(0\) \(-4\) \(-2\) \(-2\) \(+\) \(-\) \(-\) \(q-q^{3}-2q^{4}-\beta _{1}q^{5}+(-1-\beta _{2}+\beta _{3})q^{7}+\cdots\)
2001.2.a.h \(5\) \(15.978\) 5.5.312617.1 None \(-2\) \(-5\) \(-3\) \(-5\) \(+\) \(-\) \(-\) \(q-\beta _{3}q^{2}-q^{3}+(2-\beta _{1})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
2001.2.a.i \(7\) \(15.978\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-3\) \(7\) \(-3\) \(-5\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots\)
2001.2.a.j \(7\) \(15.978\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-1\) \(7\) \(-5\) \(-5\) \(-\) \(+\) \(-\) \(q-\beta _{3}q^{2}+q^{3}+(1+\beta _{4}+\beta _{5})q^{4}+(-1+\cdots)q^{5}+\cdots\)
2001.2.a.k \(10\) \(15.978\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(3\) \(-10\) \(6\) \(3\) \(+\) \(+\) \(-\) \(q+\beta _{3}q^{2}-q^{3}+(2+\beta _{6})q^{4}+(1+\beta _{4}+\cdots)q^{5}+\cdots\)
2001.2.a.l \(11\) \(15.978\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(2\) \(-11\) \(2\) \(3\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots\)
2001.2.a.m \(14\) \(15.978\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-2\) \(-14\) \(-3\) \(-3\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{11}q^{5}+\cdots\)
2001.2.a.n \(16\) \(15.978\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-1\) \(16\) \(3\) \(13\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{8}q^{5}+\cdots\)
2001.2.a.o \(20\) \(15.978\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(2\) \(20\) \(-1\) \(9\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{6}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2001))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2001)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(87))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(667))\)\(^{\oplus 2}\)