↑

Properties

Label 3002.2.a
Level $3002$
Weight $2$
Character orbit 3002.a
Rep. character $\chi_{3002}(1,\cdot)$
Character field $\Q$
Dimension $117$
Newform subspaces $14$
Sturm bound $800$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3002 = 2 \cdot 19 \cdot 79 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3002.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 14 \)
Sturm bound: \(800\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3002))\).

Total New Old
Modular forms 404 117 287
Cusp forms 397 117 280
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.

\(2\)\(19\)\(79\)FrickeDim
\(+\)\(+\)\(+\)$+$\(14\)
\(+\)\(+\)\(-\)$-$\(16\)
\(+\)\(-\)\(+\)$-$\(17\)
\(+\)\(-\)\(-\)$+$\(11\)
\(-\)\(+\)\(+\)$-$\(18\)
\(-\)\(+\)\(-\)$+$\(10\)
\(-\)\(-\)\(+\)$+$\(10\)
\(-\)\(-\)\(-\)$-$\(21\)
Plus space\(+\)\(45\)
Minus space\(-\)\(72\)

Trace form

\( 117 q + q^{2} + 4 q^{3} + 117 q^{4} + 14 q^{5} + 4 q^{6} - 4 q^{7} + q^{8} + 125 q^{9} + O(q^{10}) \) \( 117 q + q^{2} + 4 q^{3} + 117 q^{4} + 14 q^{5} + 4 q^{6} - 4 q^{7} + q^{8} + 125 q^{9} + 6 q^{10} - 4 q^{11} + 4 q^{12} - 2 q^{13} - 8 q^{15} + 117 q^{16} - 10 q^{17} - 3 q^{18} + q^{19} + 14 q^{20} + 8 q^{21} - 12 q^{22} + 12 q^{23} + 4 q^{24} + 131 q^{25} + 10 q^{26} + 40 q^{27} - 4 q^{28} + 6 q^{29} + 8 q^{30} + 24 q^{31} + q^{32} + 40 q^{33} + 2 q^{34} + 40 q^{35} + 125 q^{36} + 14 q^{37} + 5 q^{38} - 4 q^{39} + 6 q^{40} + 26 q^{41} + 12 q^{42} + 16 q^{43} - 4 q^{44} + 62 q^{45} + 16 q^{46} - 16 q^{47} + 4 q^{48} + 129 q^{49} - q^{50} + 8 q^{51} - 2 q^{52} + 22 q^{53} + 4 q^{54} - 24 q^{55} - 4 q^{57} + 14 q^{58} - 36 q^{59} - 8 q^{60} + 10 q^{61} + 8 q^{62} + 24 q^{63} + 117 q^{64} - 60 q^{65} - 16 q^{66} - 28 q^{67} - 10 q^{68} - 32 q^{69} - 24 q^{70} + 48 q^{71} - 3 q^{72} + 6 q^{73} + 18 q^{74} - 4 q^{75} + q^{76} - 24 q^{77} - 8 q^{78} - q^{79} + 14 q^{80} + 109 q^{81} + 10 q^{82} - 36 q^{83} + 8 q^{84} + 44 q^{85} - 36 q^{86} + 52 q^{87} - 12 q^{88} + 66 q^{89} - 10 q^{90} - 24 q^{91} + 12 q^{92} - 48 q^{93} - 24 q^{94} - 2 q^{95} + 4 q^{96} + 18 q^{97} + 9 q^{98} - 20 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3002))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 19 79
3002.2.a.a 3002.a 1.a $1$ $23.971$ \(\Q\) None \(-1\) \(-1\) \(0\) \(3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+3q^{7}-q^{8}+\cdots\)
3002.2.a.b 3002.a 1.a $1$ $23.971$ \(\Q\) None \(1\) \(-1\) \(3\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}+3q^{7}+\cdots\)
3002.2.a.c 3002.a 1.a $1$ $23.971$ \(\Q\) None \(1\) \(1\) \(-1\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
3002.2.a.d 3002.a 1.a $1$ $23.971$ \(\Q\) None \(1\) \(2\) \(3\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}+3q^{5}+2q^{6}+q^{8}+\cdots\)
3002.2.a.e 3002.a 1.a $2$ $23.971$ \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+\beta q^{5}-q^{6}-q^{7}+\cdots\)
3002.2.a.f 3002.a 1.a $4$ $23.971$ 4.4.10304.1 None \(-4\) \(-2\) \(-6\) \(10\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-\beta _{2}+\beta _{3})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots\)
3002.2.a.g 3002.a 1.a $8$ $23.971$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(-3\) \(-6\) \(-13\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{3}q^{3}+q^{4}+(-2+\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
3002.2.a.h 3002.a 1.a $9$ $23.971$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(9\) \(-3\) \(-3\) \(-9\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{4}q^{5}-\beta _{1}q^{6}+\cdots\)
3002.2.a.i 3002.a 1.a $11$ $23.971$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-11\) \(-4\) \(0\) \(-12\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{6}q^{5}+\beta _{1}q^{6}+\cdots\)
3002.2.a.j 3002.a 1.a $13$ $23.971$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(-13\) \(-6\) \(4\) \(-8\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{5}q^{5}+\beta _{1}q^{6}+\cdots\)
3002.2.a.k 3002.a 1.a $13$ $23.971$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(-13\) \(6\) \(8\) \(6\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{4})q^{5}-\beta _{1}q^{6}+\cdots\)
3002.2.a.l 3002.a 1.a $16$ $23.971$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-16\) \(7\) \(-2\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{5}q^{5}-\beta _{1}q^{6}+\cdots\)
3002.2.a.m 3002.a 1.a $16$ $23.971$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(16\) \(5\) \(4\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{8}q^{5}+\beta _{1}q^{6}+\cdots\)
3002.2.a.n 3002.a 1.a $21$ $23.971$ None \(21\) \(5\) \(10\) \(15\) $-$ $-$ $-$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3002))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3002)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(79))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(158))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1501))\)\(^{\oplus 2}\)