Properties

Label 5265.2.a
Level $5265$
Weight $2$
Character orbit 5265.a
Rep. character $\chi_{5265}(1,\cdot)$
Character field $\Q$
Dimension $192$
Newform subspaces $38$
Sturm bound $1512$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 5265 = 3^{4} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5265.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 38 \)
Sturm bound: \(1512\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(7\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5265))\).

Total New Old
Modular forms 780 192 588
Cusp forms 733 192 541
Eisenstein series 47 0 47

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

\(3\)\(5\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(25\)
\(+\)\(+\)\(-\)\(-\)\(25\)
\(+\)\(-\)\(+\)\(-\)\(27\)
\(+\)\(-\)\(-\)\(+\)\(19\)
\(-\)\(+\)\(+\)\(-\)\(23\)
\(-\)\(+\)\(-\)\(+\)\(23\)
\(-\)\(-\)\(+\)\(+\)\(21\)
\(-\)\(-\)\(-\)\(-\)\(29\)
Plus space\(+\)\(88\)
Minus space\(-\)\(104\)

Trace form

\( 192 q + 192 q^{4} + O(q^{10}) \) \( 192 q + 192 q^{4} + 144 q^{16} + 24 q^{19} - 24 q^{22} + 192 q^{25} - 48 q^{28} + 48 q^{34} + 24 q^{40} + 24 q^{43} + 216 q^{49} - 48 q^{58} + 24 q^{61} + 120 q^{64} - 72 q^{67} + 24 q^{70} + 72 q^{73} + 96 q^{76} - 96 q^{79} + 24 q^{82} - 72 q^{88} + 24 q^{94} + 72 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5265))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5 13
5265.2.a.a 5265.a 1.a $1$ $42.041$ \(\Q\) None \(-2\) \(0\) \(-1\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-q^{5}+2q^{10}+4q^{11}+\cdots\)
5265.2.a.b 5265.a 1.a $1$ $42.041$ \(\Q\) None \(-2\) \(0\) \(-1\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-q^{5}+2q^{10}+5q^{11}+\cdots\)
5265.2.a.c 5265.a 1.a $1$ $42.041$ \(\Q\) None \(-2\) \(0\) \(1\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+q^{5}-4q^{7}-2q^{10}+\cdots\)
5265.2.a.d 5265.a 1.a $1$ $42.041$ \(\Q\) None \(-1\) \(0\) \(-1\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-q^{5}-q^{7}+3q^{8}+q^{10}+\cdots\)
5265.2.a.e 5265.a 1.a $1$ $42.041$ \(\Q\) None \(-1\) \(0\) \(-1\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-q^{5}+2q^{7}+3q^{8}+q^{10}+\cdots\)
5265.2.a.f 5265.a 1.a $1$ $42.041$ \(\Q\) None \(-1\) \(0\) \(1\) \(3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+q^{5}+3q^{7}+3q^{8}-q^{10}+\cdots\)
5265.2.a.g 5265.a 1.a $1$ $42.041$ \(\Q\) None \(0\) \(0\) \(-1\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}-q^{5}-4q^{7}+q^{13}+4q^{16}+\cdots\)
5265.2.a.h 5265.a 1.a $1$ $42.041$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}-q^{5}+2q^{7}+3q^{11}+q^{13}+\cdots\)
5265.2.a.i 5265.a 1.a $1$ $42.041$ \(\Q\) None \(0\) \(0\) \(1\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}+q^{5}-4q^{7}+q^{13}+4q^{16}+\cdots\)
5265.2.a.j 5265.a 1.a $1$ $42.041$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}+q^{5}+2q^{7}-3q^{11}+q^{13}+\cdots\)
5265.2.a.k 5265.a 1.a $1$ $42.041$ \(\Q\) None \(1\) \(0\) \(-1\) \(3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-q^{5}+3q^{7}-3q^{8}-q^{10}+\cdots\)
5265.2.a.l 5265.a 1.a $1$ $42.041$ \(\Q\) None \(1\) \(0\) \(1\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+q^{5}-q^{7}-3q^{8}+q^{10}+\cdots\)
5265.2.a.m 5265.a 1.a $1$ $42.041$ \(\Q\) None \(1\) \(0\) \(1\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+q^{5}+2q^{7}-3q^{8}+q^{10}+\cdots\)
5265.2.a.n 5265.a 1.a $1$ $42.041$ \(\Q\) None \(2\) \(0\) \(-1\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-q^{5}-4q^{7}-2q^{10}+\cdots\)
5265.2.a.o 5265.a 1.a $1$ $42.041$ \(\Q\) None \(2\) \(0\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+q^{5}+2q^{10}-5q^{11}+\cdots\)
5265.2.a.p 5265.a 1.a $1$ $42.041$ \(\Q\) None \(2\) \(0\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+q^{5}+2q^{10}-4q^{11}+\cdots\)
5265.2.a.q 5265.a 1.a $2$ $42.041$ \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+q^{5}-\beta q^{7}+3q^{8}-q^{10}+\cdots\)
5265.2.a.r 5265.a 1.a $2$ $42.041$ \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(-2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-q^{5}+\beta q^{7}-3q^{8}-q^{10}+\cdots\)
5265.2.a.s 5265.a 1.a $3$ $42.041$ \(\Q(\zeta_{18})^+\) None \(-3\) \(0\) \(3\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
5265.2.a.t 5265.a 1.a $3$ $42.041$ \(\Q(\zeta_{18})^+\) None \(3\) \(0\) \(-3\) \(-3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
5265.2.a.u 5265.a 1.a $4$ $42.041$ 4.4.16609.1 None \(0\) \(0\) \(-4\) \(-6\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(-2-\beta _{2}+\cdots)q^{7}+\cdots\)
5265.2.a.v 5265.a 1.a $4$ $42.041$ 4.4.16609.1 None \(0\) \(0\) \(4\) \(-6\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}+(-2-\beta _{2}+\cdots)q^{7}+\cdots\)
5265.2.a.w 5265.a 1.a $6$ $42.041$ 6.6.585163476.1 None \(-2\) \(0\) \(-6\) \(4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}-q^{5}+(1+\cdots)q^{7}+\cdots\)
5265.2.a.x 5265.a 1.a $6$ $42.041$ 6.6.585163476.1 None \(2\) \(0\) \(6\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+q^{5}+(1+\cdots)q^{7}+\cdots\)
5265.2.a.y 5265.a 1.a $7$ $42.041$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-2\) \(0\) \(-7\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(-1+\beta _{4}+\cdots)q^{7}+\cdots\)
5265.2.a.z 5265.a 1.a $7$ $42.041$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(2\) \(0\) \(7\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(-1+\beta _{4}+\cdots)q^{7}+\cdots\)
5265.2.a.ba 5265.a 1.a $8$ $42.041$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-3\) \(0\) \(8\) \(-11\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
5265.2.a.bb 5265.a 1.a $8$ $42.041$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-1\) \(0\) \(8\) \(-6\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(-1+\beta _{6}+\cdots)q^{7}+\cdots\)
5265.2.a.bc 5265.a 1.a $8$ $42.041$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(-8\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(1+\beta _{3}+\cdots)q^{7}+\cdots\)
5265.2.a.bd 5265.a 1.a $8$ $42.041$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(8\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(1+\beta _{3}+\cdots)q^{7}+\cdots\)
5265.2.a.be 5265.a 1.a $8$ $42.041$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(1\) \(0\) \(-8\) \(-6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(-1+\beta _{6}+\cdots)q^{7}+\cdots\)
5265.2.a.bf 5265.a 1.a $8$ $42.041$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(3\) \(0\) \(-8\) \(-11\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
5265.2.a.bg 5265.a 1.a $13$ $42.041$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(-1\) \(0\) \(13\) \(10\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(1-\beta _{5}+\cdots)q^{7}+\cdots\)
5265.2.a.bh 5265.a 1.a $13$ $42.041$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(1\) \(0\) \(-13\) \(10\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(1-\beta _{5}+\cdots)q^{7}+\cdots\)
5265.2.a.bi 5265.a 1.a $14$ $42.041$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-2\) \(0\) \(-14\) \(4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}-\beta _{3}q^{7}+\cdots\)
5265.2.a.bj 5265.a 1.a $14$ $42.041$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(2\) \(0\) \(14\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}-\beta _{3}q^{7}+\cdots\)
5265.2.a.bk 5265.a 1.a $15$ $42.041$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-1\) \(0\) \(-15\) \(10\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(1-\beta _{6}+\cdots)q^{7}+\cdots\)
5265.2.a.bl 5265.a 1.a $15$ $42.041$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(1\) \(0\) \(15\) \(10\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(1-\beta _{6}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5265))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5265)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(135))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(195))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(351))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(405))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(585))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1053))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1755))\)\(^{\oplus 2}\)