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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2888))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 19
2888.2.a.a \(1\) \(23.061\) \(\Q\) None \(0\) \(-1\) \(-4\) \(0\) \(-\) \(-\) \(q-q^{3}-4q^{5}-2q^{9}+3q^{11}-2q^{13}+\cdots\)
2888.2.a.b \(1\) \(23.061\) \(\Q\) None \(0\) \(-1\) \(0\) \(3\) \(-\) \(-\) \(q-q^{3}+3q^{7}-2q^{9}+2q^{11}-q^{13}+\cdots\)
2888.2.a.c \(1\) \(23.061\) \(\Q\) None \(0\) \(-1\) \(3\) \(0\) \(-\) \(-\) \(q-q^{3}+3q^{5}-2q^{9}-4q^{11}+5q^{13}+\cdots\)
2888.2.a.d \(1\) \(23.061\) \(\Q\) None \(0\) \(1\) \(-4\) \(0\) \(+\) \(+\) \(q+q^{3}-4q^{5}-2q^{9}+3q^{11}+2q^{13}+\cdots\)
2888.2.a.e \(1\) \(23.061\) \(\Q\) None \(0\) \(1\) \(3\) \(0\) \(+\) \(+\) \(q+q^{3}+3q^{5}-2q^{9}-4q^{11}-5q^{13}+\cdots\)
2888.2.a.f \(1\) \(23.061\) \(\Q\) None \(0\) \(2\) \(-1\) \(-3\) \(-\) \(-\) \(q+2q^{3}-q^{5}-3q^{7}+q^{9}-3q^{11}+\cdots\)
2888.2.a.g \(2\) \(23.061\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(5\) \(-4\) \(-\) \(-\) \(q-2\beta q^{3}+(2+\beta )q^{5}-2q^{7}+(1+4\beta )q^{9}+\cdots\)
2888.2.a.h \(2\) \(23.061\) \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(-3\) \(2\) \(-\) \(+\) \(q-\beta q^{3}+(-1-\beta )q^{5}+q^{7}+(1+\beta )q^{9}+\cdots\)
2888.2.a.i \(2\) \(23.061\) \(\Q(\sqrt{5}) \) None \(0\) \(-1\) \(-2\) \(4\) \(-\) \(-\) \(q-\beta q^{3}-2\beta q^{5}+(3-2\beta )q^{7}+(-2+\cdots)q^{9}+\cdots\)
2888.2.a.j \(2\) \(23.061\) \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(-3\) \(2\) \(+\) \(+\) \(q+\beta q^{3}+(-1-\beta )q^{5}+q^{7}+(1+\beta )q^{9}+\cdots\)
2888.2.a.k \(2\) \(23.061\) \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(-2\) \(4\) \(+\) \(-\) \(q+\beta q^{3}-2\beta q^{5}+(3-2\beta )q^{7}+(-2+\cdots)q^{9}+\cdots\)
2888.2.a.l \(2\) \(23.061\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(5\) \(-4\) \(+\) \(-\) \(q+2\beta q^{3}+(2+\beta )q^{5}-2q^{7}+(1+4\beta )q^{9}+\cdots\)
2888.2.a.m \(3\) \(23.061\) \(\Q(\zeta_{18})^+\) None \(0\) \(-3\) \(-3\) \(-6\) \(-\) \(-\) \(q+(-1-2\beta _{1}+\beta _{2})q^{3}+(-1-\beta _{2})q^{5}+\cdots\)
2888.2.a.n \(3\) \(23.061\) 3.3.316.1 None \(0\) \(-1\) \(1\) \(-2\) \(+\) \(-\) \(q+(-\beta _{1}+\beta _{2})q^{3}+\beta _{1}q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
2888.2.a.o \(3\) \(23.061\) 3.3.961.1 None \(0\) \(-1\) \(1\) \(4\) \(+\) \(-\) \(q-\beta _{1}q^{3}-\beta _{2}q^{5}+(2-\beta _{1}+\beta _{2})q^{7}+\cdots\)
2888.2.a.p \(3\) \(23.061\) \(\Q(\zeta_{18})^+\) None \(0\) \(0\) \(0\) \(-3\) \(-\) \(-\) \(q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+(-1-2\beta _{1}+\cdots)q^{7}+\cdots\)
2888.2.a.q \(3\) \(23.061\) \(\Q(\zeta_{18})^+\) None \(0\) \(0\) \(0\) \(-3\) \(+\) \(+\) \(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+(-1-2\beta _{1}+\cdots)q^{7}+\cdots\)
2888.2.a.r \(3\) \(23.061\) 3.3.316.1 None \(0\) \(1\) \(1\) \(-2\) \(-\) \(+\) \(q+(\beta _{1}-\beta _{2})q^{3}+\beta _{1}q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
2888.2.a.s \(3\) \(23.061\) \(\Q(\zeta_{18})^+\) None \(0\) \(3\) \(-3\) \(-6\) \(+\) \(+\) \(q+(1+2\beta _{1}-\beta _{2})q^{3}+(-1-\beta _{2})q^{5}+\cdots\)
2888.2.a.t \(6\) \(23.061\) 6.6.3022625.1 None \(0\) \(-3\) \(2\) \(-2\) \(-\) \(-\) \(q+(-1-\beta _{2})q^{3}+(-\beta _{1}-\beta _{5})q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots\)
2888.2.a.u \(6\) \(23.061\) 6.6.3022625.1 None \(0\) \(3\) \(2\) \(-2\) \(+\) \(-\) \(q+(1+\beta _{2})q^{3}+(-\beta _{1}-\beta _{5})q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots\)
2888.2.a.v \(8\) \(23.061\) 8.8.\(\cdots\).1 None \(0\) \(-6\) \(-2\) \(-2\) \(+\) \(+\) \(q+(-1+\beta _{1})q^{3}+(-1+\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots\)
2888.2.a.w \(8\) \(23.061\) 8.8.\(\cdots\).1 None \(0\) \(6\) \(-2\) \(-2\) \(-\) \(+\) \(q+(1-\beta _{1})q^{3}+(-1+\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots\)
2888.2.a.x \(9\) \(23.061\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-3\) \(3\) \(9\) \(+\) \(-\) \(q-\beta _{1}q^{3}+(\beta _{4}+\beta _{5})q^{5}+(1+\beta _{6})q^{7}+\cdots\)
2888.2.a.y \(9\) \(23.061\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(3\) \(3\) \(9\) \(-\) \(+\) \(q+\beta _{1}q^{3}+(\beta _{4}+\beta _{5})q^{5}+(1+\beta _{6})q^{7}+\cdots\)

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

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