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

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

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

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 23 29
2001.2.a.a 2001.a 1.a $1$ $15.978$ \(\Q\) None \(-1\) \(-1\) \(3\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+3q^{5}+q^{6}+3q^{8}+\cdots\)
2001.2.a.b 2001.a 1.a $1$ $15.978$ \(\Q\) None \(0\) \(-1\) \(4\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+4q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots\)
2001.2.a.c 2001.a 1.a $1$ $15.978$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}+q^{9}-4q^{11}-2q^{12}+\cdots\)
2001.2.a.d 2001.a 1.a $2$ $15.978$ \(\Q(\sqrt{5}) \) None \(-2\) \(-2\) \(-4\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}+3q^{8}+\cdots\)
2001.2.a.e 2001.a 1.a $2$ $15.978$ \(\Q(\sqrt{6}) \) None \(0\) \(2\) \(0\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-\beta q^{5}+(-2+\beta )q^{7}+\cdots\)
2001.2.a.f 2001.a 1.a $2$ $15.978$ \(\Q(\sqrt{17}) \) None \(2\) \(-2\) \(-3\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
2001.2.a.g 2001.a 1.a $4$ $15.978$ 4.4.5744.1 None \(0\) \(-4\) \(-2\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-\beta _{1}q^{5}+(-1-\beta _{2}+\beta _{3})q^{7}+\cdots\)
2001.2.a.h 2001.a 1.a $5$ $15.978$ 5.5.312617.1 None \(-2\) \(-5\) \(-3\) \(-5\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{2}-q^{3}+(2-\beta _{1})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
2001.2.a.i 2001.a 1.a $7$ $15.978$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-3\) \(7\) \(-3\) \(-5\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots\)
2001.2.a.j 2001.a 1.a $7$ $15.978$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-1\) \(7\) \(-5\) \(-5\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{2}+q^{3}+(1+\beta _{4}+\beta _{5})q^{4}+(-1+\cdots)q^{5}+\cdots\)
2001.2.a.k 2001.a 1.a $10$ $15.978$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(3\) \(-10\) \(6\) \(3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}-q^{3}+(2+\beta _{6})q^{4}+(1+\beta _{4}+\cdots)q^{5}+\cdots\)
2001.2.a.l 2001.a 1.a $11$ $15.978$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(2\) \(-11\) \(2\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots\)
2001.2.a.m 2001.a 1.a $14$ $15.978$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-2\) \(-14\) \(-3\) \(-3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{11}q^{5}+\cdots\)
2001.2.a.n 2001.a 1.a $16$ $15.978$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-1\) \(16\) \(3\) \(13\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{8}q^{5}+\cdots\)
2001.2.a.o 2001.a 1.a $20$ $15.978$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(2\) \(20\) \(-1\) \(9\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{6}q^{5}+\cdots\)

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

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