Properties

Label 1003.2.a
Level 1003
Weight 2
Character orbit a
Rep. character \(\chi_{1003}(1,\cdot)\)
Character field \(\Q\)
Dimension 77
Newforms 10
Sturm bound 180
Trace bound 2

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Defining parameters

Level: \( N \) = \( 1003 = 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1003.a (trivial)
Character field: \(\Q\)
Newforms: \( 10 \)
Sturm bound: \(180\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1003))\).

Total New Old
Modular forms 92 77 15
Cusp forms 89 77 12
Eisenstein series 3 0 3

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

\(17\)\(59\)FrickeDim.
\(+\)\(+\)\(+\)\(18\)
\(+\)\(-\)\(-\)\(22\)
\(-\)\(+\)\(-\)\(20\)
\(-\)\(-\)\(+\)\(17\)
Plus space\(+\)\(35\)
Minus space\(-\)\(42\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1003))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 17 59
1003.2.a.a \(1\) \(8.009\) \(\Q\) None \(-1\) \(3\) \(1\) \(1\) \(-\) \(+\) \(q-q^{2}+3q^{3}-q^{4}+q^{5}-3q^{6}+q^{7}+\cdots\)
1003.2.a.b \(1\) \(8.009\) \(\Q\) None \(0\) \(2\) \(-2\) \(2\) \(+\) \(+\) \(q+2q^{3}-2q^{4}-2q^{5}+2q^{7}+q^{9}+\cdots\)
1003.2.a.c \(1\) \(8.009\) \(\Q\) None \(1\) \(1\) \(1\) \(3\) \(-\) \(+\) \(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}+3q^{7}+\cdots\)
1003.2.a.d \(1\) \(8.009\) \(\Q\) None \(2\) \(0\) \(-2\) \(-2\) \(-\) \(-\) \(q+2q^{2}+2q^{4}-2q^{5}-2q^{7}-3q^{9}+\cdots\)
1003.2.a.e \(3\) \(8.009\) 3.3.229.1 None \(-3\) \(2\) \(-4\) \(-2\) \(+\) \(+\) \(q-q^{2}+(1+\beta _{2})q^{3}-q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
1003.2.a.f \(4\) \(8.009\) 4.4.2225.1 None \(-3\) \(-2\) \(1\) \(8\) \(+\) \(+\) \(q+(-1+\beta _{1})q^{2}+\beta _{2}q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1003.2.a.g \(10\) \(8.009\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-1\) \(-7\) \(-12\) \(-9\) \(+\) \(+\) \(q-\beta _{8}q^{2}+(-1+\beta _{1})q^{3}+(2-\beta _{5})q^{4}+\cdots\)
1003.2.a.h \(16\) \(8.009\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-6\) \(-7\) \(-21\) \(-11\) \(-\) \(-\) \(q-\beta _{1}q^{2}-\beta _{10}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1003.2.a.i \(18\) \(8.009\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(5\) \(1\) \(21\) \(-1\) \(-\) \(+\) \(q+\beta _{1}q^{2}+\beta _{10}q^{3}+(1+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
1003.2.a.j \(22\) \(8.009\) None \(5\) \(7\) \(19\) \(3\) \(+\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1003))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1003)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(59))\)\(^{\oplus 2}\)