Properties

Label 3008.2.a
Level $3008$
Weight $2$
Character orbit 3008.a
Rep. character $\chi_{3008}(1,\cdot)$
Character field $\Q$
Dimension $92$
Newform subspaces $26$
Sturm bound $768$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 3008 = 2^{6} \cdot 47 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3008.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 26 \)
Sturm bound: \(768\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3008))\).

Total New Old
Modular forms 396 92 304
Cusp forms 373 92 281
Eisenstein series 23 0 23

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

\(2\)\(47\)FrickeDim
\(+\)\(+\)$+$\(21\)
\(+\)\(-\)$-$\(26\)
\(-\)\(+\)$-$\(25\)
\(-\)\(-\)$+$\(20\)
Plus space\(+\)\(41\)
Minus space\(-\)\(51\)

Trace form

\( 92 q + 92 q^{9} + O(q^{10}) \) \( 92 q + 92 q^{9} + 16 q^{13} - 8 q^{17} + 16 q^{21} + 84 q^{25} - 16 q^{29} - 16 q^{33} - 24 q^{41} + 92 q^{49} - 16 q^{53} - 16 q^{57} + 16 q^{61} + 8 q^{73} - 16 q^{77} + 76 q^{81} + 8 q^{89} + 16 q^{93} - 40 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3008))\) 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 47
3008.2.a.a 3008.a 1.a $1$ $24.019$ \(\Q\) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{9}-2q^{11}+4q^{13}-2q^{17}+2q^{19}+\cdots\)
3008.2.a.b 3008.a 1.a $1$ $24.019$ \(\Q\) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{9}+2q^{11}+4q^{13}-2q^{17}-2q^{19}+\cdots\)
3008.2.a.c 3008.a 1.a $2$ $24.019$ \(\Q(\sqrt{5}) \) None \(0\) \(-3\) \(2\) \(7\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(2-2\beta )q^{5}+(4-\beta )q^{7}+\cdots\)
3008.2.a.d 3008.a 1.a $2$ $24.019$ \(\Q(\sqrt{13}) \) None \(0\) \(-1\) \(0\) \(5\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(3-\beta )q^{7}+\beta q^{9}+(-2+2\beta )q^{11}+\cdots\)
3008.2.a.e 3008.a 1.a $2$ $24.019$ \(\Q(\sqrt{5}) \) None \(0\) \(-1\) \(2\) \(3\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(2-2\beta )q^{5}+(1+\beta )q^{7}+(-2+\cdots)q^{9}+\cdots\)
3008.2.a.f 3008.a 1.a $2$ $24.019$ \(\Q(\sqrt{5}) \) None \(0\) \(-1\) \(4\) \(-1\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+2q^{5}+(1-3\beta )q^{7}+(-2+\beta )q^{9}+\cdots\)
3008.2.a.g 3008.a 1.a $2$ $24.019$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-4\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2\beta q^{3}+(-2-\beta )q^{5}+(-2+2\beta )q^{7}+\cdots\)
3008.2.a.h 3008.a 1.a $2$ $24.019$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-4\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2\beta q^{3}+(-2+\beta )q^{5}+(2+2\beta )q^{7}+\cdots\)
3008.2.a.i 3008.a 1.a $2$ $24.019$ \(\Q(\sqrt{13}) \) None \(0\) \(1\) \(0\) \(-5\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-3+\beta )q^{7}+\beta q^{9}+(2-2\beta )q^{11}+\cdots\)
3008.2.a.j 3008.a 1.a $2$ $24.019$ \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(2\) \(-3\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(2-2\beta )q^{5}+(-1-\beta )q^{7}+\cdots\)
3008.2.a.k 3008.a 1.a $2$ $24.019$ \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(4\) \(1\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+2q^{5}+(-1+3\beta )q^{7}+(-2+\cdots)q^{9}+\cdots\)
3008.2.a.l 3008.a 1.a $2$ $24.019$ \(\Q(\sqrt{5}) \) None \(0\) \(3\) \(2\) \(-7\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(2-2\beta )q^{5}+(-4+\beta )q^{7}+\cdots\)
3008.2.a.m 3008.a 1.a $4$ $24.019$ 4.4.13448.1 None \(0\) \(-3\) \(0\) \(5\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{3})q^{3}+(-\beta _{1}+\beta _{2}-\beta _{3})q^{5}+\cdots\)
3008.2.a.n 3008.a 1.a $4$ $24.019$ 4.4.4752.1 None \(0\) \(-2\) \(4\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(1+\beta _{2})q^{5}+(-1-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
3008.2.a.o 3008.a 1.a $4$ $24.019$ 4.4.7625.1 None \(0\) \(-1\) \(-4\) \(3\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1+\beta _{2})q^{5}+(1+\beta _{1}+\beta _{3})q^{7}+\cdots\)
3008.2.a.p 3008.a 1.a $4$ $24.019$ 4.4.1957.1 None \(0\) \(0\) \(2\) \(-4\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+(1-\beta _{1}-\beta _{3})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
3008.2.a.q 3008.a 1.a $4$ $24.019$ 4.4.1957.1 None \(0\) \(0\) \(2\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+(1-\beta _{1}-\beta _{3})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
3008.2.a.r 3008.a 1.a $4$ $24.019$ 4.4.7625.1 None \(0\) \(1\) \(-4\) \(-3\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-1+\beta _{2})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
3008.2.a.s 3008.a 1.a $4$ $24.019$ 4.4.4752.1 None \(0\) \(2\) \(4\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1+\beta _{2})q^{5}+(1+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
3008.2.a.t 3008.a 1.a $4$ $24.019$ 4.4.13448.1 None \(0\) \(3\) \(0\) \(-5\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+(\beta _{1}-\beta _{2}+\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
3008.2.a.u 3008.a 1.a $5$ $24.019$ 5.5.617072.1 None \(0\) \(0\) \(-2\) \(-8\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{4}q^{3}+(-1+\beta _{1}+\beta _{3}-\beta _{4})q^{5}+\cdots\)
3008.2.a.v 3008.a 1.a $5$ $24.019$ 5.5.617072.1 None \(0\) \(0\) \(-2\) \(8\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{4}q^{3}+(-1+\beta _{1}+\beta _{3}-\beta _{4})q^{5}+\cdots\)
3008.2.a.w 3008.a 1.a $6$ $24.019$ 6.6.66862976.1 None \(0\) \(-4\) \(2\) \(-4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+\beta _{5}q^{5}+(\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)
3008.2.a.x 3008.a 1.a $6$ $24.019$ 6.6.66862976.1 None \(0\) \(4\) \(2\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+\beta _{5}q^{5}+(-\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
3008.2.a.y 3008.a 1.a $8$ $24.019$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-2\) \(-6\) \(-8\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{3}+(-1-\beta _{7})q^{5}+(-1-\beta _{6}+\cdots)q^{7}+\cdots\)
3008.2.a.z 3008.a 1.a $8$ $24.019$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(2\) \(-6\) \(8\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{3}+(-1-\beta _{7})q^{5}+(1+\beta _{6})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3008))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3008)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(47))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(94))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(188))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(376))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(752))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1504))\)\(^{\oplus 2}\)