Properties

Label 2288.2.a
Level $2288$
Weight $2$
Character orbit 2288.a
Rep. character $\chi_{2288}(1,\cdot)$
Character field $\Q$
Dimension $60$
Newform subspaces $27$
Sturm bound $672$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 2288 = 2^{4} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2288.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 27 \)
Sturm bound: \(672\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(3\), \(5\), \(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2288))\).

Total New Old
Modular forms 348 60 288
Cusp forms 325 60 265
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.

\(2\)\(11\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(9\)
\(+\)\(+\)\(-\)\(-\)\(9\)
\(+\)\(-\)\(+\)\(-\)\(6\)
\(+\)\(-\)\(-\)\(+\)\(6\)
\(-\)\(+\)\(+\)\(-\)\(10\)
\(-\)\(+\)\(-\)\(+\)\(5\)
\(-\)\(-\)\(+\)\(+\)\(5\)
\(-\)\(-\)\(-\)\(-\)\(10\)
Plus space\(+\)\(25\)
Minus space\(-\)\(35\)

Trace form

\( 60q + 60q^{9} + O(q^{10}) \) \( 60q + 60q^{9} - 6q^{11} - 4q^{15} + 16q^{19} + 16q^{21} + 60q^{25} - 12q^{27} + 16q^{29} + 28q^{31} + 24q^{35} + 16q^{45} + 32q^{47} + 60q^{49} + 56q^{51} - 36q^{59} - 32q^{61} - 32q^{63} + 12q^{67} - 16q^{69} + 4q^{71} - 28q^{75} + 16q^{79} + 44q^{81} + 16q^{83} - 32q^{85} + 56q^{87} - 16q^{89} - 12q^{91} - 72q^{95} - 18q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2288))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 11 13
2288.2.a.a \(1\) \(18.270\) \(\Q\) None \(0\) \(-3\) \(3\) \(3\) \(+\) \(+\) \(+\) \(q-3q^{3}+3q^{5}+3q^{7}+6q^{9}-q^{11}+\cdots\)
2288.2.a.b \(1\) \(18.270\) \(\Q\) None \(0\) \(-2\) \(-1\) \(-1\) \(-\) \(-\) \(+\) \(q-2q^{3}-q^{5}-q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
2288.2.a.c \(1\) \(18.270\) \(\Q\) None \(0\) \(-2\) \(1\) \(3\) \(-\) \(+\) \(-\) \(q-2q^{3}+q^{5}+3q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
2288.2.a.d \(1\) \(18.270\) \(\Q\) None \(0\) \(-2\) \(3\) \(-1\) \(+\) \(-\) \(+\) \(q-2q^{3}+3q^{5}-q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
2288.2.a.e \(1\) \(18.270\) \(\Q\) None \(0\) \(-1\) \(-1\) \(2\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+2q^{7}-2q^{9}-q^{11}-q^{13}+\cdots\)
2288.2.a.f \(1\) \(18.270\) \(\Q\) None \(0\) \(-1\) \(-1\) \(2\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+2q^{7}-2q^{9}-q^{11}+q^{13}+\cdots\)
2288.2.a.g \(1\) \(18.270\) \(\Q\) None \(0\) \(-1\) \(3\) \(-2\) \(-\) \(+\) \(-\) \(q-q^{3}+3q^{5}-2q^{7}-2q^{9}-q^{11}+\cdots\)
2288.2.a.h \(1\) \(18.270\) \(\Q\) None \(0\) \(1\) \(-3\) \(5\) \(-\) \(-\) \(-\) \(q+q^{3}-3q^{5}+5q^{7}-2q^{9}+q^{11}+\cdots\)
2288.2.a.i \(1\) \(18.270\) \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) \(-\) \(-\) \(+\) \(q+q^{3}-q^{5}-q^{7}-2q^{9}+q^{11}-q^{13}+\cdots\)
2288.2.a.j \(1\) \(18.270\) \(\Q\) None \(0\) \(1\) \(-1\) \(2\) \(-\) \(-\) \(+\) \(q+q^{3}-q^{5}+2q^{7}-2q^{9}+q^{11}-q^{13}+\cdots\)
2288.2.a.k \(1\) \(18.270\) \(\Q\) None \(0\) \(1\) \(1\) \(-3\) \(-\) \(+\) \(-\) \(q+q^{3}+q^{5}-3q^{7}-2q^{9}-q^{11}+q^{13}+\cdots\)
2288.2.a.l \(1\) \(18.270\) \(\Q\) None \(0\) \(2\) \(3\) \(1\) \(-\) \(-\) \(-\) \(q+2q^{3}+3q^{5}+q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
2288.2.a.m \(2\) \(18.270\) \(\Q(\sqrt{21}) \) None \(0\) \(-1\) \(-4\) \(-3\) \(-\) \(+\) \(-\) \(q-\beta q^{3}-2q^{5}+(-1-\beta )q^{7}+(2+\beta )q^{9}+\cdots\)
2288.2.a.n \(2\) \(18.270\) \(\Q(\sqrt{21}) \) None \(0\) \(-1\) \(4\) \(-5\) \(-\) \(-\) \(+\) \(q-\beta q^{3}+2q^{5}+(-3+\beta )q^{7}+(2+\beta )q^{9}+\cdots\)
2288.2.a.o \(2\) \(18.270\) \(\Q(\sqrt{5}) \) None \(0\) \(3\) \(-2\) \(-1\) \(+\) \(+\) \(+\) \(q+(1+\beta )q^{3}-2\beta q^{5}-\beta q^{7}+(-1+3\beta )q^{9}+\cdots\)
2288.2.a.p \(2\) \(18.270\) \(\Q(\sqrt{5}) \) None \(0\) \(3\) \(-2\) \(-1\) \(+\) \(+\) \(-\) \(q+(1+\beta )q^{3}+(-2+2\beta )q^{5}+(-2+3\beta )q^{7}+\cdots\)
2288.2.a.q \(2\) \(18.270\) \(\Q(\sqrt{5}) \) None \(0\) \(3\) \(-2\) \(5\) \(+\) \(-\) \(+\) \(q+(1+\beta )q^{3}+(-2+2\beta )q^{5}+(2+\beta )q^{7}+\cdots\)
2288.2.a.r \(2\) \(18.270\) \(\Q(\sqrt{13}) \) None \(0\) \(3\) \(0\) \(3\) \(-\) \(-\) \(-\) \(q+(1+\beta )q^{3}+(2-\beta )q^{7}+(1+3\beta )q^{9}+\cdots\)
2288.2.a.s \(3\) \(18.270\) 3.3.229.1 None \(0\) \(-3\) \(1\) \(-6\) \(+\) \(-\) \(-\) \(q+(-1-\beta _{1})q^{3}+(\beta _{1}-\beta _{2})q^{5}+(-2+\cdots)q^{7}+\cdots\)
2288.2.a.t \(3\) \(18.270\) 3.3.961.1 None \(0\) \(-1\) \(2\) \(4\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+(2-\beta _{1}+\beta _{2})q^{7}+\cdots\)
2288.2.a.u \(3\) \(18.270\) 3.3.229.1 None \(0\) \(0\) \(-5\) \(-2\) \(+\) \(-\) \(-\) \(q+\beta _{1}q^{3}+(-2+\beta _{1}-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
2288.2.a.v \(3\) \(18.270\) 3.3.229.1 None \(0\) \(0\) \(1\) \(4\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+(1-\beta _{2})q^{7}+\cdots\)
2288.2.a.w \(3\) \(18.270\) 3.3.229.1 None \(0\) \(2\) \(-1\) \(7\) \(-\) \(+\) \(+\) \(q+(1+\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(2+2\beta _{1}+\cdots)q^{7}+\cdots\)
2288.2.a.x \(4\) \(18.270\) 4.4.1957.1 None \(0\) \(0\) \(0\) \(-6\) \(-\) \(+\) \(+\) \(q+\beta _{2}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+(-2+\beta _{3})q^{7}+\cdots\)
2288.2.a.y \(5\) \(18.270\) 5.5.7698829.1 None \(0\) \(0\) \(-4\) \(-6\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{3}+(-1-\beta _{3})q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots\)
2288.2.a.z \(6\) \(18.270\) 6.6.194616205.1 None \(0\) \(-3\) \(1\) \(-4\) \(-\) \(-\) \(-\) \(q+(-1-\beta _{1})q^{3}+\beta _{4}q^{5}+(-1-\beta _{5})q^{7}+\cdots\)
2288.2.a.ba \(6\) \(18.270\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(1\) \(5\) \(1\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{3}+(1-\beta _{2})q^{5}-\beta _{5}q^{7}+(2+\beta _{4}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2288))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2288)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(286))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(572))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1144))\)\(^{\oplus 2}\)