Properties

Label 1007.2.a
Level 1007
Weight 2
Character orbit a
Rep. character \(\chi_{1007}(1,\cdot)\)
Character field \(\Q\)
Dimension 79
Newforms 5
Sturm bound 180
Trace bound 2

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Defining parameters

Level: \( N \) = \( 1007 = 19 \cdot 53 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1007.a (trivial)
Character field: \(\Q\)
Newforms: \( 5 \)
Sturm bound: \(180\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1007))\).

Total New Old
Modular forms 92 79 13
Cusp forms 89 79 10
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.

\(19\)\(53\)FrickeDim.
\(+\)\(+\)\(+\)\(13\)
\(+\)\(-\)\(-\)\(28\)
\(-\)\(+\)\(-\)\(26\)
\(-\)\(-\)\(+\)\(12\)
Plus space\(+\)\(25\)
Minus space\(-\)\(54\)

Trace form

\(79q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 85q^{4} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 75q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(79q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 85q^{4} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 75q^{9} \) \(\mathstrut +\mathstrut 2q^{10} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 14q^{13} \) \(\mathstrut +\mathstrut 16q^{15} \) \(\mathstrut +\mathstrut 77q^{16} \) \(\mathstrut +\mathstrut 16q^{17} \) \(\mathstrut +\mathstrut 27q^{18} \) \(\mathstrut -\mathstrut 3q^{19} \) \(\mathstrut +\mathstrut 6q^{20} \) \(\mathstrut -\mathstrut 20q^{21} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 8q^{23} \) \(\mathstrut -\mathstrut 12q^{24} \) \(\mathstrut +\mathstrut 107q^{25} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut -\mathstrut 20q^{27} \) \(\mathstrut -\mathstrut 8q^{28} \) \(\mathstrut -\mathstrut 2q^{29} \) \(\mathstrut -\mathstrut 16q^{30} \) \(\mathstrut +\mathstrut 16q^{31} \) \(\mathstrut +\mathstrut 39q^{32} \) \(\mathstrut +\mathstrut 36q^{33} \) \(\mathstrut -\mathstrut 34q^{34} \) \(\mathstrut -\mathstrut 14q^{35} \) \(\mathstrut +\mathstrut 101q^{36} \) \(\mathstrut +\mathstrut 26q^{37} \) \(\mathstrut +\mathstrut 3q^{38} \) \(\mathstrut -\mathstrut 40q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut +\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 28q^{42} \) \(\mathstrut +\mathstrut 2q^{43} \) \(\mathstrut +\mathstrut 28q^{44} \) \(\mathstrut +\mathstrut 32q^{45} \) \(\mathstrut +\mathstrut 12q^{46} \) \(\mathstrut +\mathstrut 34q^{47} \) \(\mathstrut -\mathstrut 28q^{48} \) \(\mathstrut +\mathstrut 101q^{49} \) \(\mathstrut +\mathstrut 41q^{50} \) \(\mathstrut -\mathstrut 4q^{51} \) \(\mathstrut +\mathstrut 2q^{52} \) \(\mathstrut +\mathstrut q^{53} \) \(\mathstrut -\mathstrut 56q^{54} \) \(\mathstrut -\mathstrut 22q^{55} \) \(\mathstrut -\mathstrut 8q^{56} \) \(\mathstrut +\mathstrut 4q^{57} \) \(\mathstrut +\mathstrut 18q^{58} \) \(\mathstrut -\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 52q^{60} \) \(\mathstrut +\mathstrut 16q^{61} \) \(\mathstrut -\mathstrut 44q^{62} \) \(\mathstrut +\mathstrut 54q^{63} \) \(\mathstrut +\mathstrut 69q^{64} \) \(\mathstrut +\mathstrut 4q^{65} \) \(\mathstrut -\mathstrut 56q^{66} \) \(\mathstrut +\mathstrut 52q^{67} \) \(\mathstrut +\mathstrut 2q^{68} \) \(\mathstrut +\mathstrut 28q^{69} \) \(\mathstrut +\mathstrut 28q^{70} \) \(\mathstrut -\mathstrut 12q^{71} \) \(\mathstrut +\mathstrut 23q^{72} \) \(\mathstrut +\mathstrut 20q^{73} \) \(\mathstrut +\mathstrut 2q^{74} \) \(\mathstrut -\mathstrut 16q^{75} \) \(\mathstrut -\mathstrut 3q^{76} \) \(\mathstrut -\mathstrut 2q^{77} \) \(\mathstrut -\mathstrut 12q^{78} \) \(\mathstrut +\mathstrut 8q^{79} \) \(\mathstrut +\mathstrut 46q^{80} \) \(\mathstrut +\mathstrut 79q^{81} \) \(\mathstrut +\mathstrut 26q^{82} \) \(\mathstrut -\mathstrut 44q^{83} \) \(\mathstrut -\mathstrut 24q^{84} \) \(\mathstrut +\mathstrut 6q^{85} \) \(\mathstrut +\mathstrut 16q^{86} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut +\mathstrut 36q^{88} \) \(\mathstrut -\mathstrut 6q^{89} \) \(\mathstrut -\mathstrut 82q^{90} \) \(\mathstrut -\mathstrut 40q^{91} \) \(\mathstrut -\mathstrut 12q^{92} \) \(\mathstrut +\mathstrut 16q^{93} \) \(\mathstrut -\mathstrut 44q^{94} \) \(\mathstrut +\mathstrut 4q^{95} \) \(\mathstrut -\mathstrut 116q^{96} \) \(\mathstrut +\mathstrut 42q^{97} \) \(\mathstrut +\mathstrut 99q^{98} \) \(\mathstrut -\mathstrut 6q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1007))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 19 53
1007.2.a.a \(1\) \(8.041\) \(\Q\) None \(2\) \(0\) \(-3\) \(-1\) \(+\) \(+\) \(q+2q^{2}+2q^{4}-3q^{5}-q^{7}-3q^{9}+\cdots\)
1007.2.a.b \(12\) \(8.041\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-5\) \(1\) \(-4\) \(-8\) \(+\) \(+\) \(q-\beta _{1}q^{2}-\beta _{10}q^{3}+(\beta _{1}+\beta _{2})q^{4}+\beta _{6}q^{5}+\cdots\)
1007.2.a.c \(12\) \(8.041\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-3\) \(-5\) \(-2\) \(-8\) \(-\) \(-\) \(q-\beta _{1}q^{2}-\beta _{9}q^{3}+(1+\beta _{2})q^{4}+\beta _{7}q^{5}+\cdots\)
1007.2.a.d \(26\) \(8.041\) None \(6\) \(9\) \(4\) \(8\) \(-\) \(+\)
1007.2.a.e \(28\) \(8.041\) None \(3\) \(-1\) \(5\) \(15\) \(+\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1007))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1007)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(53))\)\(^{\oplus 2}\)