Properties

Label 3009.2.a
Level 3009
Weight 2
Character orbit a
Rep. character \(\chi_{3009}(1,\cdot)\)
Character field \(\Q\)
Dimension 155
Newforms 11
Sturm bound 720
Trace bound 5

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 3009 = 3 \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3009.a (trivial)
Character field: \(\Q\)
Newforms: \( 11 \)
Sturm bound: \(720\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3009))\).

Total New Old
Modular forms 364 155 209
Cusp forms 357 155 202
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.

\(3\)\(17\)\(59\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(19\)
\(+\)\(+\)\(-\)\(-\)\(21\)
\(+\)\(-\)\(+\)\(-\)\(20\)
\(+\)\(-\)\(-\)\(+\)\(16\)
\(-\)\(+\)\(+\)\(-\)\(24\)
\(-\)\(+\)\(-\)\(+\)\(14\)
\(-\)\(-\)\(+\)\(+\)\(15\)
\(-\)\(-\)\(-\)\(-\)\(26\)
Plus space\(+\)\(64\)
Minus space\(-\)\(91\)

Trace form

\(155q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 161q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 155q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(155q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 161q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 155q^{9} \) \(\mathstrut -\mathstrut 18q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut 5q^{12} \) \(\mathstrut +\mathstrut 6q^{13} \) \(\mathstrut -\mathstrut 16q^{14} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 161q^{16} \) \(\mathstrut -\mathstrut q^{17} \) \(\mathstrut +\mathstrut 5q^{18} \) \(\mathstrut -\mathstrut 2q^{20} \) \(\mathstrut +\mathstrut 16q^{21} \) \(\mathstrut +\mathstrut 28q^{22} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut -\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 137q^{25} \) \(\mathstrut +\mathstrut 14q^{26} \) \(\mathstrut +\mathstrut 3q^{27} \) \(\mathstrut -\mathstrut 8q^{28} \) \(\mathstrut +\mathstrut 2q^{29} \) \(\mathstrut -\mathstrut 18q^{30} \) \(\mathstrut +\mathstrut 33q^{32} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 3q^{34} \) \(\mathstrut -\mathstrut 24q^{35} \) \(\mathstrut +\mathstrut 161q^{36} \) \(\mathstrut +\mathstrut 42q^{37} \) \(\mathstrut -\mathstrut 44q^{38} \) \(\mathstrut +\mathstrut 10q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut +\mathstrut 12q^{44} \) \(\mathstrut -\mathstrut 6q^{45} \) \(\mathstrut +\mathstrut 48q^{46} \) \(\mathstrut +\mathstrut 32q^{47} \) \(\mathstrut -\mathstrut 3q^{48} \) \(\mathstrut +\mathstrut 147q^{49} \) \(\mathstrut +\mathstrut 107q^{50} \) \(\mathstrut +\mathstrut 7q^{51} \) \(\mathstrut +\mathstrut 70q^{52} \) \(\mathstrut -\mathstrut 14q^{53} \) \(\mathstrut -\mathstrut 3q^{54} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut +\mathstrut 28q^{57} \) \(\mathstrut -\mathstrut 42q^{58} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut +\mathstrut 14q^{60} \) \(\mathstrut -\mathstrut 14q^{61} \) \(\mathstrut +\mathstrut 48q^{62} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 185q^{64} \) \(\mathstrut -\mathstrut 60q^{65} \) \(\mathstrut +\mathstrut 4q^{66} \) \(\mathstrut -\mathstrut 20q^{67} \) \(\mathstrut -\mathstrut 7q^{68} \) \(\mathstrut -\mathstrut 20q^{69} \) \(\mathstrut -\mathstrut 8q^{70} \) \(\mathstrut +\mathstrut 9q^{72} \) \(\mathstrut -\mathstrut 26q^{73} \) \(\mathstrut -\mathstrut 18q^{74} \) \(\mathstrut -\mathstrut 3q^{75} \) \(\mathstrut +\mathstrut 28q^{76} \) \(\mathstrut -\mathstrut 40q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut +\mathstrut 40q^{79} \) \(\mathstrut -\mathstrut 2q^{80} \) \(\mathstrut +\mathstrut 155q^{81} \) \(\mathstrut -\mathstrut 22q^{82} \) \(\mathstrut +\mathstrut 4q^{83} \) \(\mathstrut +\mathstrut 40q^{84} \) \(\mathstrut +\mathstrut 6q^{85} \) \(\mathstrut +\mathstrut 52q^{86} \) \(\mathstrut +\mathstrut 2q^{87} \) \(\mathstrut +\mathstrut 28q^{88} \) \(\mathstrut -\mathstrut 26q^{89} \) \(\mathstrut -\mathstrut 18q^{90} \) \(\mathstrut -\mathstrut 16q^{91} \) \(\mathstrut +\mathstrut 96q^{92} \) \(\mathstrut +\mathstrut 24q^{93} \) \(\mathstrut -\mathstrut 56q^{94} \) \(\mathstrut +\mathstrut 16q^{95} \) \(\mathstrut -\mathstrut 23q^{96} \) \(\mathstrut +\mathstrut 30q^{97} \) \(\mathstrut -\mathstrut 107q^{98} \) \(\mathstrut +\mathstrut 4q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3009))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 17 59
3009.2.a.a \(1\) \(24.027\) \(\Q\) None \(0\) \(1\) \(-1\) \(2\) \(-\) \(-\) \(+\) \(q+q^{3}-2q^{4}-q^{5}+2q^{7}+q^{9}-5q^{11}+\cdots\)
3009.2.a.b \(2\) \(24.027\) \(\Q(\sqrt{5}) \) None \(-1\) \(-2\) \(-3\) \(-4\) \(+\) \(-\) \(+\) \(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-1-\beta )q^{5}+\cdots\)
3009.2.a.c \(2\) \(24.027\) \(\Q(\sqrt{5}) \) None \(-1\) \(-2\) \(3\) \(4\) \(+\) \(+\) \(+\) \(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(1+\beta )q^{5}+\cdots\)
3009.2.a.d \(14\) \(24.027\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-4\) \(14\) \(-3\) \(-11\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{10}q^{5}+\cdots\)
3009.2.a.e \(14\) \(24.027\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(14\) \(-5\) \(-11\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}-\beta _{11}q^{5}-\beta _{1}q^{6}+\cdots\)
3009.2.a.f \(16\) \(24.027\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-4\) \(-16\) \(-3\) \(-3\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{9}q^{5}+\cdots\)
3009.2.a.g \(17\) \(24.027\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(1\) \(-17\) \(-11\) \(-5\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{6}+\cdots)q^{5}+\cdots\)
3009.2.a.h \(18\) \(24.027\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(7\) \(-18\) \(2\) \(3\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{15}q^{5}+\cdots\)
3009.2.a.i \(21\) \(24.027\) None \(2\) \(-21\) \(10\) \(1\) \(+\) \(+\) \(-\)
3009.2.a.j \(24\) \(24.027\) None \(2\) \(24\) \(-3\) \(19\) \(-\) \(+\) \(+\)
3009.2.a.k \(26\) \(24.027\) None \(3\) \(26\) \(8\) \(13\) \(-\) \(-\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3009))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3009)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(59))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(177))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1003))\)\(^{\oplus 2}\)