Properties

Label 1502.2.a
Level 1502
Weight 2
Character orbit a
Rep. character \(\chi_{1502}(1,\cdot)\)
Character field \(\Q\)
Dimension 63
Newforms 8
Sturm bound 376
Trace bound 3

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Defining parameters

Level: \( N \) = \( 1502 = 2 \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1502.a (trivial)
Character field: \(\Q\)
Newforms: \( 8 \)
Sturm bound: \(376\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1502))\).

Total New Old
Modular forms 190 63 127
Cusp forms 187 63 124
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.

\(2\)\(751\)FrickeDim.
\(+\)\(+\)\(+\)\(13\)
\(+\)\(-\)\(-\)\(19\)
\(-\)\(+\)\(-\)\(18\)
\(-\)\(-\)\(+\)\(13\)
Plus space\(+\)\(26\)
Minus space\(-\)\(37\)

Trace form

\( 63q - q^{2} + 2q^{3} + 63q^{4} - 2q^{5} - 2q^{6} + 4q^{7} - q^{8} + 67q^{9} + O(q^{10}) \) \( 63q - q^{2} + 2q^{3} + 63q^{4} - 2q^{5} - 2q^{6} + 4q^{7} - q^{8} + 67q^{9} - 2q^{10} - 2q^{11} + 2q^{12} - 6q^{13} - 4q^{14} + 4q^{15} + 63q^{16} - 10q^{17} + 3q^{18} - 2q^{20} + 8q^{21} - 6q^{22} + 16q^{23} - 2q^{24} + 65q^{25} - 2q^{26} - 4q^{27} + 4q^{28} - 4q^{29} + 12q^{31} - q^{32} - 8q^{33} - 6q^{34} - 28q^{35} + 67q^{36} - 6q^{37} + 4q^{38} + 12q^{39} - 2q^{40} - 6q^{41} - 4q^{42} - 12q^{43} - 2q^{44} - 14q^{45} - 16q^{46} - 36q^{47} + 2q^{48} + 51q^{49} + q^{50} - 12q^{51} - 6q^{52} - 34q^{53} - 20q^{54} - 16q^{55} - 4q^{56} - 20q^{57} - 4q^{59} + 4q^{60} - 10q^{61} - 20q^{62} + 24q^{63} + 63q^{64} - 4q^{65} + 8q^{66} + 2q^{67} - 10q^{68} + 32q^{69} + 16q^{71} + 3q^{72} + 18q^{73} - 18q^{74} - 38q^{75} - 4q^{77} + 56q^{79} - 2q^{80} + 71q^{81} - 14q^{82} + 14q^{83} + 8q^{84} - 20q^{85} - 16q^{86} - 36q^{87} - 6q^{88} - 34q^{89} - 46q^{90} + 12q^{91} + 16q^{92} + 40q^{93} - 4q^{94} - 2q^{96} - 34q^{97} - 9q^{98} + 6q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1502))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 751
1502.2.a.a \(1\) \(11.994\) \(\Q\) None \(1\) \(-2\) \(2\) \(4\) \(-\) \(+\) \(q+q^{2}-2q^{3}+q^{4}+2q^{5}-2q^{6}+4q^{7}+\cdots\)
1502.2.a.b \(1\) \(11.994\) \(\Q\) None \(1\) \(1\) \(2\) \(4\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+4q^{7}+\cdots\)
1502.2.a.c \(2\) \(11.994\) \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-3\) \(-3\) \(+\) \(+\) \(q-q^{2}+(1-2\beta )q^{3}+q^{4}+(-2+\beta )q^{5}+\cdots\)
1502.2.a.d \(2\) \(11.994\) \(\Q(\sqrt{5}) \) None \(2\) \(-1\) \(2\) \(-6\) \(-\) \(-\) \(q+q^{2}-\beta q^{3}+q^{4}+q^{5}-\beta q^{6}+(-4+\cdots)q^{7}+\cdots\)
1502.2.a.e \(11\) \(11.994\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-11\) \(-4\) \(1\) \(-6\) \(+\) \(+\) \(q-q^{2}+\beta _{10}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
1502.2.a.f \(11\) \(11.994\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(11\) \(-11\) \(-12\) \(-9\) \(-\) \(-\) \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1-\beta _{7}+\cdots)q^{5}+\cdots\)
1502.2.a.g \(16\) \(11.994\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(16\) \(13\) \(4\) \(7\) \(-\) \(+\) \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+\beta _{8}q^{5}+(1+\cdots)q^{6}+\cdots\)
1502.2.a.h \(19\) \(11.994\) \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None \(-19\) \(6\) \(2\) \(13\) \(+\) \(-\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{3}q^{5}-\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1502))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1502)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(751))\)\(^{\oplus 2}\)