Properties

Label 2888.2.a
Level $2888$
Weight $2$
Character orbit 2888.a
Rep. character $\chi_{2888}(1,\cdot)$
Character field $\Q$
Dimension $85$
Newform subspaces $25$
Sturm bound $760$
Trace bound $15$

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Defining parameters

Level: \( N \) \(=\) \( 2888 = 2^{3} \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2888.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 25 \)
Sturm bound: \(760\)
Trace bound: \(15\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2888))\).

Total New Old
Modular forms 420 85 335
Cusp forms 341 85 256
Eisenstein series 79 0 79

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

\(2\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(18\)
\(+\)\(-\)\(-\)\(25\)
\(-\)\(+\)\(-\)\(22\)
\(-\)\(-\)\(+\)\(20\)
Plus space\(+\)\(38\)
Minus space\(-\)\(47\)

Trace form

\( 85 q - 4 q^{7} + 79 q^{9} + O(q^{10}) \) \( 85 q - 4 q^{7} + 79 q^{9} + 6 q^{11} - 2 q^{13} + 8 q^{15} - 2 q^{17} + 93 q^{25} + 10 q^{29} - 12 q^{31} + 4 q^{33} + 14 q^{37} + 16 q^{39} - 6 q^{41} - 2 q^{43} + 28 q^{45} + 24 q^{47} + 81 q^{49} + 4 q^{51} - 2 q^{53} - 28 q^{55} + 8 q^{59} - 8 q^{61} - 32 q^{63} - 16 q^{65} - 28 q^{67} + 44 q^{69} + 8 q^{71} + 6 q^{73} - 36 q^{75} - 4 q^{77} - 12 q^{79} + 53 q^{81} - 14 q^{83} - 12 q^{85} + 16 q^{87} - 6 q^{89} - 32 q^{91} + 16 q^{93} - 22 q^{97} + 58 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2888))\) 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
2888.2.a.a 2888.a 1.a $1$ $23.061$ \(\Q\) None \(0\) \(-1\) \(-4\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{5}-2q^{9}+3q^{11}-2q^{13}+\cdots\)
2888.2.a.b 2888.a 1.a $1$ $23.061$ \(\Q\) None \(0\) \(-1\) \(0\) \(3\) $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{7}-2q^{9}+2q^{11}-q^{13}+\cdots\)
2888.2.a.c 2888.a 1.a $1$ $23.061$ \(\Q\) None \(0\) \(-1\) \(3\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{5}-2q^{9}-4q^{11}+5q^{13}+\cdots\)
2888.2.a.d 2888.a 1.a $1$ $23.061$ \(\Q\) None \(0\) \(1\) \(-4\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{5}-2q^{9}+3q^{11}+2q^{13}+\cdots\)
2888.2.a.e 2888.a 1.a $1$ $23.061$ \(\Q\) None \(0\) \(1\) \(3\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{5}-2q^{9}-4q^{11}-5q^{13}+\cdots\)
2888.2.a.f 2888.a 1.a $1$ $23.061$ \(\Q\) None \(0\) \(2\) \(-1\) \(-3\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{5}-3q^{7}+q^{9}-3q^{11}+\cdots\)
2888.2.a.g 2888.a 1.a $2$ $23.061$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(5\) \(-4\) $-$ $-$ $\mathrm{SU}(2)$ \(q-2\beta q^{3}+(2+\beta )q^{5}-2q^{7}+(1+4\beta )q^{9}+\cdots\)
2888.2.a.h 2888.a 1.a $2$ $23.061$ \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(-3\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-1-\beta )q^{5}+q^{7}+(1+\beta )q^{9}+\cdots\)
2888.2.a.i 2888.a 1.a $2$ $23.061$ \(\Q(\sqrt{5}) \) None \(0\) \(-1\) \(-2\) \(4\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-2\beta q^{5}+(3-2\beta )q^{7}+(-2+\cdots)q^{9}+\cdots\)
2888.2.a.j 2888.a 1.a $2$ $23.061$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(-3\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-1-\beta )q^{5}+q^{7}+(1+\beta )q^{9}+\cdots\)
2888.2.a.k 2888.a 1.a $2$ $23.061$ \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(-2\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-2\beta q^{5}+(3-2\beta )q^{7}+(-2+\cdots)q^{9}+\cdots\)
2888.2.a.l 2888.a 1.a $2$ $23.061$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(5\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2\beta q^{3}+(2+\beta )q^{5}-2q^{7}+(1+4\beta )q^{9}+\cdots\)
2888.2.a.m 2888.a 1.a $3$ $23.061$ \(\Q(\zeta_{18})^+\) None \(0\) \(-3\) \(-3\) \(-6\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-2\beta _{1}+\beta _{2})q^{3}+(-1-\beta _{2})q^{5}+\cdots\)
2888.2.a.n 2888.a 1.a $3$ $23.061$ 3.3.316.1 None \(0\) \(-1\) \(1\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}+\beta _{2})q^{3}+\beta _{1}q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
2888.2.a.o 2888.a 1.a $3$ $23.061$ 3.3.961.1 None \(0\) \(-1\) \(1\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-\beta _{2}q^{5}+(2-\beta _{1}+\beta _{2})q^{7}+\cdots\)
2888.2.a.p 2888.a 1.a $3$ $23.061$ \(\Q(\zeta_{18})^+\) None \(0\) \(0\) \(0\) \(-3\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+(-1-2\beta _{1}+\cdots)q^{7}+\cdots\)
2888.2.a.q 2888.a 1.a $3$ $23.061$ \(\Q(\zeta_{18})^+\) None \(0\) \(0\) \(0\) \(-3\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+(-1-2\beta _{1}+\cdots)q^{7}+\cdots\)
2888.2.a.r 2888.a 1.a $3$ $23.061$ 3.3.316.1 None \(0\) \(1\) \(1\) \(-2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}-\beta _{2})q^{3}+\beta _{1}q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
2888.2.a.s 2888.a 1.a $3$ $23.061$ \(\Q(\zeta_{18})^+\) None \(0\) \(3\) \(-3\) \(-6\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+2\beta _{1}-\beta _{2})q^{3}+(-1-\beta _{2})q^{5}+\cdots\)
2888.2.a.t 2888.a 1.a $6$ $23.061$ 6.6.3022625.1 None \(0\) \(-3\) \(2\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+(-\beta _{1}-\beta _{5})q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots\)
2888.2.a.u 2888.a 1.a $6$ $23.061$ 6.6.3022625.1 None \(0\) \(3\) \(2\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+(-\beta _{1}-\beta _{5})q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots\)
2888.2.a.v 2888.a 1.a $8$ $23.061$ 8.8.\(\cdots\).1 None \(0\) \(-6\) \(-2\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-1+\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots\)
2888.2.a.w 2888.a 1.a $8$ $23.061$ 8.8.\(\cdots\).1 None \(0\) \(6\) \(-2\) \(-2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(-1+\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots\)
2888.2.a.x 2888.a 1.a $9$ $23.061$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-3\) \(3\) \(9\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(\beta _{4}+\beta _{5})q^{5}+(1+\beta _{6})q^{7}+\cdots\)
2888.2.a.y 2888.a 1.a $9$ $23.061$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(3\) \(3\) \(9\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(\beta _{4}+\beta _{5})q^{5}+(1+\beta _{6})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2888))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2888)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(722))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1444))\)\(^{\oplus 2}\)