Properties

Label 8005.2.a
Level 8005
Weight 2
Character orbit a
Rep. character \(\chi_{8005}(1,\cdot)\)
Character field \(\Q\)
Dimension 533
Newforms 8
Sturm bound 1602
Trace bound 3

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 8005 = 5 \cdot 1601 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8005.a (trivial)
Character field: \(\Q\)
Newforms: \( 8 \)
Sturm bound: \(1602\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8005))\).

Total New Old
Modular forms 802 533 269
Cusp forms 799 533 266
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.

\(5\)\(1601\)FrickeDim.
\(+\)\(+\)\(+\)\(127\)
\(+\)\(-\)\(-\)\(139\)
\(-\)\(+\)\(-\)\(139\)
\(-\)\(-\)\(+\)\(128\)
Plus space\(+\)\(255\)
Minus space\(-\)\(278\)

Trace form

\(533q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut +\mathstrut 527q^{4} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 537q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(533q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut +\mathstrut 527q^{4} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 537q^{9} \) \(\mathstrut -\mathstrut q^{10} \) \(\mathstrut +\mathstrut 4q^{12} \) \(\mathstrut -\mathstrut 10q^{13} \) \(\mathstrut +\mathstrut 4q^{14} \) \(\mathstrut -\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 503q^{16} \) \(\mathstrut +\mathstrut 2q^{17} \) \(\mathstrut -\mathstrut 9q^{18} \) \(\mathstrut -\mathstrut q^{20} \) \(\mathstrut -\mathstrut 16q^{21} \) \(\mathstrut -\mathstrut 24q^{22} \) \(\mathstrut -\mathstrut 16q^{23} \) \(\mathstrut +\mathstrut 533q^{25} \) \(\mathstrut -\mathstrut 2q^{26} \) \(\mathstrut -\mathstrut 24q^{27} \) \(\mathstrut -\mathstrut 36q^{28} \) \(\mathstrut -\mathstrut 14q^{29} \) \(\mathstrut +\mathstrut 8q^{30} \) \(\mathstrut -\mathstrut 28q^{31} \) \(\mathstrut -\mathstrut 9q^{32} \) \(\mathstrut -\mathstrut 26q^{34} \) \(\mathstrut -\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 539q^{36} \) \(\mathstrut -\mathstrut 14q^{37} \) \(\mathstrut +\mathstrut 24q^{38} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut -\mathstrut 9q^{40} \) \(\mathstrut +\mathstrut 26q^{41} \) \(\mathstrut +\mathstrut 56q^{42} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 16q^{44} \) \(\mathstrut +\mathstrut 13q^{45} \) \(\mathstrut -\mathstrut 12q^{46} \) \(\mathstrut +\mathstrut 28q^{47} \) \(\mathstrut +\mathstrut 28q^{48} \) \(\mathstrut +\mathstrut 533q^{49} \) \(\mathstrut -\mathstrut q^{50} \) \(\mathstrut +\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 82q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 68q^{54} \) \(\mathstrut -\mathstrut 4q^{55} \) \(\mathstrut +\mathstrut 32q^{56} \) \(\mathstrut +\mathstrut 4q^{57} \) \(\mathstrut -\mathstrut 54q^{58} \) \(\mathstrut +\mathstrut 16q^{59} \) \(\mathstrut -\mathstrut 34q^{61} \) \(\mathstrut +\mathstrut 4q^{62} \) \(\mathstrut +\mathstrut 12q^{63} \) \(\mathstrut +\mathstrut 431q^{64} \) \(\mathstrut +\mathstrut 2q^{65} \) \(\mathstrut +\mathstrut 56q^{66} \) \(\mathstrut -\mathstrut 12q^{67} \) \(\mathstrut +\mathstrut 26q^{68} \) \(\mathstrut -\mathstrut 4q^{69} \) \(\mathstrut +\mathstrut 12q^{70} \) \(\mathstrut -\mathstrut 16q^{71} \) \(\mathstrut -\mathstrut 29q^{72} \) \(\mathstrut -\mathstrut 26q^{73} \) \(\mathstrut -\mathstrut 50q^{74} \) \(\mathstrut -\mathstrut 12q^{76} \) \(\mathstrut -\mathstrut 40q^{77} \) \(\mathstrut +\mathstrut 76q^{78} \) \(\mathstrut -\mathstrut 24q^{79} \) \(\mathstrut -\mathstrut q^{80} \) \(\mathstrut +\mathstrut 557q^{81} \) \(\mathstrut -\mathstrut 14q^{82} \) \(\mathstrut +\mathstrut 20q^{83} \) \(\mathstrut -\mathstrut 32q^{84} \) \(\mathstrut -\mathstrut 18q^{85} \) \(\mathstrut +\mathstrut 20q^{86} \) \(\mathstrut -\mathstrut 8q^{87} \) \(\mathstrut -\mathstrut 104q^{88} \) \(\mathstrut +\mathstrut 34q^{89} \) \(\mathstrut +\mathstrut 7q^{90} \) \(\mathstrut -\mathstrut 48q^{91} \) \(\mathstrut -\mathstrut 96q^{92} \) \(\mathstrut -\mathstrut 76q^{93} \) \(\mathstrut -\mathstrut 64q^{94} \) \(\mathstrut +\mathstrut 4q^{95} \) \(\mathstrut +\mathstrut 116q^{96} \) \(\mathstrut -\mathstrut 2q^{97} \) \(\mathstrut +\mathstrut 43q^{98} \) \(\mathstrut +\mathstrut 24q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8005))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5 1601
8005.2.a.a \(1\) \(63.920\) \(\Q\) None \(-1\) \(-2\) \(1\) \(2\) \(-\) \(-\) \(q-q^{2}-2q^{3}-q^{4}+q^{5}+2q^{6}+2q^{7}+\cdots\)
8005.2.a.b \(1\) \(63.920\) \(\Q\) None \(-1\) \(2\) \(1\) \(2\) \(-\) \(-\) \(q-q^{2}+2q^{3}-q^{4}+q^{5}-2q^{6}+2q^{7}+\cdots\)
8005.2.a.c \(2\) \(63.920\) \(\Q(\sqrt{5}) \) None \(-1\) \(-2\) \(2\) \(-3\) \(-\) \(+\) \(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots\)
8005.2.a.d \(2\) \(63.920\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-2\) \(0\) \(+\) \(-\) \(q+q^{2}+\beta q^{3}-q^{4}-q^{5}+\beta q^{6}-\beta q^{7}+\cdots\)
8005.2.a.e \(126\) \(63.920\) None \(-15\) \(-46\) \(126\) \(-60\) \(-\) \(-\)
8005.2.a.f \(127\) \(63.920\) None \(-6\) \(-18\) \(-127\) \(28\) \(+\) \(+\)
8005.2.a.g \(137\) \(63.920\) None \(4\) \(20\) \(-137\) \(-30\) \(+\) \(-\)
8005.2.a.h \(137\) \(63.920\) None \(17\) \(46\) \(137\) \(53\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8005))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8005)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(1601))\)\(^{\oplus 2}\)