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Properties

Label 3006.2.a
Level $3006$
Weight $2$
Character orbit 3006.a
Rep. character $\chi_{3006}(1,\cdot)$
Character field $\Q$
Dimension $70$
Newform subspaces $23$
Sturm bound $1008$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 3006 = 2 \cdot 3^{2} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3006.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 23 \)
Sturm bound: \(1008\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3006))\).

Total New Old
Modular forms 512 70 442
Cusp forms 497 70 427
Eisenstein series 15 0 15

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(167\)FrickeDim
\(+\)\(+\)\(+\)$+$\(4\)
\(+\)\(+\)\(-\)$-$\(10\)
\(+\)\(-\)\(+\)$-$\(12\)
\(+\)\(-\)\(-\)$+$\(9\)
\(-\)\(+\)\(+\)$-$\(10\)
\(-\)\(+\)\(-\)$+$\(4\)
\(-\)\(-\)\(+\)$+$\(9\)
\(-\)\(-\)\(-\)$-$\(12\)
Plus space\(+\)\(26\)
Minus space\(-\)\(44\)

Trace form

\( 70 q + 70 q^{4} - 2 q^{5} + O(q^{10}) \) \( 70 q + 70 q^{4} - 2 q^{5} + 2 q^{10} - 2 q^{13} + 4 q^{14} + 70 q^{16} - 4 q^{17} - 2 q^{20} + 4 q^{22} + 4 q^{23} + 70 q^{25} - 10 q^{26} + 4 q^{29} - 12 q^{31} - 4 q^{34} - 16 q^{35} + 10 q^{37} + 16 q^{38} + 2 q^{40} - 12 q^{41} + 6 q^{43} + 16 q^{46} + 40 q^{47} + 98 q^{49} - 2 q^{52} - 2 q^{53} - 20 q^{55} + 4 q^{56} - 6 q^{59} + 4 q^{61} - 8 q^{62} + 70 q^{64} + 40 q^{65} + 6 q^{67} - 4 q^{68} + 8 q^{70} + 28 q^{71} - 12 q^{73} + 10 q^{74} + 8 q^{77} + 48 q^{79} - 2 q^{80} + 12 q^{82} + 10 q^{83} - 12 q^{85} + 6 q^{86} + 4 q^{88} + 32 q^{91} + 4 q^{92} - 12 q^{94} - 8 q^{95} - 8 q^{97} + 16 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3006))\) 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 3 167
3006.2.a.a 3006.a 1.a $1$ $24.003$ \(\Q\) None \(-1\) \(0\) \(-3\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-3q^{5}+q^{7}-q^{8}+3q^{10}+\cdots\)
3006.2.a.b 3006.a 1.a $1$ $24.003$ \(\Q\) None \(-1\) \(0\) \(3\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+3q^{5}-3q^{7}-q^{8}-3q^{10}+\cdots\)
3006.2.a.c 3006.a 1.a $1$ $24.003$ \(\Q\) None \(1\) \(0\) \(-3\) \(3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-3q^{5}+3q^{7}+q^{8}-3q^{10}+\cdots\)
3006.2.a.d 3006.a 1.a $1$ $24.003$ \(\Q\) None \(1\) \(0\) \(-2\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{5}-4q^{7}+q^{8}-2q^{10}+\cdots\)
3006.2.a.e 3006.a 1.a $1$ $24.003$ \(\Q\) None \(1\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{8}-4q^{13}+q^{16}-6q^{17}+\cdots\)
3006.2.a.f 3006.a 1.a $1$ $24.003$ \(\Q\) None \(1\) \(0\) \(1\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
3006.2.a.g 3006.a 1.a $2$ $24.003$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-2\) \(-6\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+(-3-\beta )q^{7}-q^{8}+\cdots\)
3006.2.a.h 3006.a 1.a $2$ $24.003$ \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(4\) \(-6\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(1+2\beta )q^{5}-3q^{7}-q^{8}+\cdots\)
3006.2.a.i 3006.a 1.a $2$ $24.003$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(4\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(2+\beta )q^{5}-q^{8}+(-2+\cdots)q^{10}+\cdots\)
3006.2.a.j 3006.a 1.a $2$ $24.003$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-4\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-2+\beta )q^{5}+q^{8}+(-2+\cdots)q^{10}+\cdots\)
3006.2.a.k 3006.a 1.a $2$ $24.003$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-2\) \(-6\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-1+\beta )q^{5}-3q^{7}+q^{8}+\cdots\)
3006.2.a.l 3006.a 1.a $2$ $24.003$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(2\) \(-6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+(-3-\beta )q^{7}+q^{8}+\cdots\)
3006.2.a.m 3006.a 1.a $2$ $24.003$ \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+(-1+2\beta )q^{7}+q^{8}+\cdots\)
3006.2.a.n 3006.a 1.a $2$ $24.003$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(2+\beta )q^{5}+2\beta q^{7}+q^{8}+\cdots\)
3006.2.a.o 3006.a 1.a $3$ $24.003$ 3.3.148.1 None \(-3\) \(0\) \(3\) \(-5\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(1-\beta _{2})q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots\)
3006.2.a.p 3006.a 1.a $3$ $24.003$ 3.3.733.1 None \(-3\) \(0\) \(3\) \(3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
3006.2.a.q 3006.a 1.a $3$ $24.003$ 3.3.1300.1 None \(3\) \(0\) \(-3\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-1+\beta _{1})q^{5}+(\beta _{1}-\beta _{2})q^{7}+\cdots\)
3006.2.a.r 3006.a 1.a $3$ $24.003$ 3.3.469.1 None \(3\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(\beta _{1}+\beta _{2})q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots\)
3006.2.a.s 3006.a 1.a $4$ $24.003$ 4.4.2777.1 None \(-4\) \(0\) \(-5\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-1+\beta _{1})q^{5}+(\beta _{2}-\beta _{3})q^{7}+\cdots\)
3006.2.a.t 3006.a 1.a $5$ $24.003$ 5.5.11256624.1 None \(5\) \(0\) \(1\) \(9\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-\beta _{2}q^{5}+(2-\beta _{4})q^{7}+q^{8}+\cdots\)
3006.2.a.u 3006.a 1.a $7$ $24.003$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(0\) \(-5\) \(7\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-1+\beta _{1})q^{5}+(1-\beta _{3}+\cdots)q^{7}+\cdots\)
3006.2.a.v 3006.a 1.a $10$ $24.003$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-10\) \(0\) \(-4\) \(6\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-\beta _{1}q^{5}+(1-\beta _{4})q^{7}-q^{8}+\cdots\)
3006.2.a.w 3006.a 1.a $10$ $24.003$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(10\) \(0\) \(4\) \(6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta _{1}q^{5}+(1-\beta _{4})q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3006))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3006)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(167))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(334))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(501))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1002))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1503))\)\(^{\oplus 2}\)