Properties

Label 2752.2.a
Level $2752$
Weight $2$
Character orbit 2752.a
Rep. character $\chi_{2752}(1,\cdot)$
Character field $\Q$
Dimension $84$
Newform subspaces $30$
Sturm bound $704$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 2752 = 2^{6} \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2752.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 30 \)
Sturm bound: \(704\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2752))\).

Total New Old
Modular forms 364 84 280
Cusp forms 341 84 257
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.

\(2\)\(43\)FrickeDim
\(+\)\(+\)$+$\(20\)
\(+\)\(-\)$-$\(23\)
\(-\)\(+\)$-$\(22\)
\(-\)\(-\)$+$\(19\)
Plus space\(+\)\(39\)
Minus space\(-\)\(45\)

Trace form

\( 84 q + 84 q^{9} + O(q^{10}) \) \( 84 q + 84 q^{9} - 8 q^{17} + 76 q^{25} - 8 q^{41} + 48 q^{45} + 84 q^{49} + 48 q^{53} - 32 q^{61} + 16 q^{69} + 8 q^{73} + 84 q^{81} - 32 q^{85} + 8 q^{89} - 40 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2752))\) 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 43
2752.2.a.a 2752.a 1.a $1$ $21.975$ \(\Q\) None \(0\) \(-2\) \(0\) \(4\) $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+4q^{7}+q^{9}-3q^{11}+q^{13}+\cdots\)
2752.2.a.b 2752.a 1.a $1$ $21.975$ \(\Q\) None \(0\) \(-2\) \(4\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+4q^{5}+q^{9}+3q^{11}+5q^{13}+\cdots\)
2752.2.a.c 2752.a 1.a $1$ $21.975$ \(\Q\) None \(0\) \(0\) \(2\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-2q^{7}-3q^{9}-q^{11}+q^{13}+\cdots\)
2752.2.a.d 2752.a 1.a $1$ $21.975$ \(\Q\) None \(0\) \(0\) \(2\) \(2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+2q^{7}-3q^{9}+q^{11}+q^{13}+\cdots\)
2752.2.a.e 2752.a 1.a $1$ $21.975$ \(\Q\) None \(0\) \(2\) \(0\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-4q^{7}+q^{9}+3q^{11}+q^{13}+\cdots\)
2752.2.a.f 2752.a 1.a $1$ $21.975$ \(\Q\) None \(0\) \(2\) \(4\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+4q^{5}+q^{9}-3q^{11}+5q^{13}+\cdots\)
2752.2.a.g 2752.a 1.a $2$ $21.975$ \(\Q(\sqrt{2}) \) None \(0\) \(-4\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-2+\beta )q^{3}-\beta q^{5}+\beta q^{7}+(3-4\beta )q^{9}+\cdots\)
2752.2.a.h 2752.a 1.a $2$ $21.975$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(2\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+(1+\beta )q^{5}+(1+\beta )q^{7}+\cdots\)
2752.2.a.i 2752.a 1.a $2$ $21.975$ \(\Q(\sqrt{21}) \) None \(0\) \(-1\) \(-3\) \(-4\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-1-\beta )q^{5}-2q^{7}+(2+\beta )q^{9}+\cdots\)
2752.2.a.j 2752.a 1.a $2$ $21.975$ \(\Q(\sqrt{21}) \) None \(0\) \(-1\) \(1\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(1-\beta )q^{5}+2q^{7}+(2+\beta )q^{9}+\cdots\)
2752.2.a.k 2752.a 1.a $2$ $21.975$ \(\Q(\sqrt{5}) \) None \(0\) \(-1\) \(3\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(1+\beta )q^{5}+(2-4\beta )q^{7}+(-2+\cdots)q^{9}+\cdots\)
2752.2.a.l 2752.a 1.a $2$ $21.975$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-4\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-2+\beta )q^{5}+(-2+\beta )q^{7}+\cdots\)
2752.2.a.m 2752.a 1.a $2$ $21.975$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-4\) \(4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-2-\beta )q^{5}+(2+\beta )q^{7}-q^{9}+\cdots\)
2752.2.a.n 2752.a 1.a $2$ $21.975$ \(\Q(\sqrt{21}) \) None \(0\) \(1\) \(-3\) \(4\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-1-\beta )q^{5}+2q^{7}+(2+\beta )q^{9}+\cdots\)
2752.2.a.o 2752.a 1.a $2$ $21.975$ \(\Q(\sqrt{21}) \) None \(0\) \(1\) \(1\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(1-\beta )q^{5}-2q^{7}+(2+\beta )q^{9}+\cdots\)
2752.2.a.p 2752.a 1.a $2$ $21.975$ \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(3\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(1+\beta )q^{5}+(-2+4\beta )q^{7}+\cdots\)
2752.2.a.q 2752.a 1.a $2$ $21.975$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(2\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(1-\beta )q^{5}+(-1+\beta )q^{7}+\cdots\)
2752.2.a.r 2752.a 1.a $2$ $21.975$ \(\Q(\sqrt{2}) \) None \(0\) \(4\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{3}+\beta q^{5}+\beta q^{7}+(3+4\beta )q^{9}+\cdots\)
2752.2.a.s 2752.a 1.a $3$ $21.975$ 3.3.229.1 None \(0\) \(-3\) \(-1\) \(6\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+\beta _{2}q^{5}+2q^{7}+(1+\cdots)q^{9}+\cdots\)
2752.2.a.t 2752.a 1.a $3$ $21.975$ 3.3.148.1 None \(0\) \(-2\) \(2\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(1-\beta _{1})q^{5}+(-1+\cdots)q^{7}+\cdots\)
2752.2.a.u 2752.a 1.a $3$ $21.975$ 3.3.148.1 None \(0\) \(2\) \(2\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(1-\beta _{1})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
2752.2.a.v 2752.a 1.a $3$ $21.975$ 3.3.229.1 None \(0\) \(3\) \(-1\) \(-6\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+\beta _{2}q^{5}-2q^{7}+(1-2\beta _{1}+\cdots)q^{9}+\cdots\)
2752.2.a.w 2752.a 1.a $5$ $21.975$ 5.5.386404.1 None \(0\) \(-5\) \(-1\) \(4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1}+\beta _{2})q^{3}+(-\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
2752.2.a.x 2752.a 1.a $5$ $21.975$ 5.5.7998268.1 None \(0\) \(-1\) \(-1\) \(-2\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+\beta _{4}q^{5}+(-1+\beta _{2}-\beta _{4})q^{7}+\cdots\)
2752.2.a.y 2752.a 1.a $5$ $21.975$ 5.5.792644.1 None \(0\) \(-1\) \(1\) \(-8\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(\beta _{1}+\beta _{4})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
2752.2.a.z 2752.a 1.a $5$ $21.975$ 5.5.7998268.1 None \(0\) \(1\) \(-1\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+\beta _{4}q^{5}+(1-\beta _{2}+\beta _{4})q^{7}+\cdots\)
2752.2.a.ba 2752.a 1.a $5$ $21.975$ 5.5.792644.1 None \(0\) \(1\) \(1\) \(8\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{4})q^{5}+(1+\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)
2752.2.a.bb 2752.a 1.a $5$ $21.975$ 5.5.386404.1 None \(0\) \(5\) \(-1\) \(-4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1}-\beta _{2})q^{3}+(-\beta _{2}-\beta _{3})q^{5}+\cdots\)
2752.2.a.bc 2752.a 1.a $6$ $21.975$ 6.6.550669316.1 None \(0\) \(-5\) \(-5\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-1-\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots\)
2752.2.a.bd 2752.a 1.a $6$ $21.975$ 6.6.550669316.1 None \(0\) \(5\) \(-5\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(-1-\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2752))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2752)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(172))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(43))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(86))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(344))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(688))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1376))\)\(^{\oplus 2}\)