Properties

Label 5472.2.a
Level $5472$
Weight $2$
Character orbit 5472.a
Rep. character $\chi_{5472}(1,\cdot)$
Character field $\Q$
Dimension $90$
Newform subspaces $48$
Sturm bound $1920$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 5472 = 2^{5} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5472.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 48 \)
Sturm bound: \(1920\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\), \(13\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5472))\).

Total New Old
Modular forms 992 90 902
Cusp forms 929 90 839
Eisenstein series 63 0 63

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

\(2\)\(3\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(9\)
\(+\)\(+\)\(-\)\(-\)\(9\)
\(+\)\(-\)\(+\)\(-\)\(15\)
\(+\)\(-\)\(-\)\(+\)\(12\)
\(-\)\(+\)\(+\)\(-\)\(9\)
\(-\)\(+\)\(-\)\(+\)\(9\)
\(-\)\(-\)\(+\)\(+\)\(12\)
\(-\)\(-\)\(-\)\(-\)\(15\)
Plus space\(+\)\(42\)
Minus space\(-\)\(48\)

Trace form

\( 90 q + 4 q^{5} + O(q^{10}) \) \( 90 q + 4 q^{5} + 4 q^{13} - 12 q^{17} + 62 q^{25} - 12 q^{29} + 4 q^{37} - 12 q^{41} + 74 q^{49} + 52 q^{53} + 4 q^{61} - 24 q^{65} - 28 q^{73} - 56 q^{77} - 16 q^{85} + 36 q^{89} + 36 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5472))\) 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 3 19
5472.2.a.a 5472.a 1.a $1$ $43.694$ \(\Q\) None \(0\) \(0\) \(-3\) \(-5\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{5}-5q^{7}+5q^{11}-4q^{13}+3q^{17}+\cdots\)
5472.2.a.b 5472.a 1.a $1$ $43.694$ \(\Q\) None \(0\) \(0\) \(-3\) \(-3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-3q^{5}-3q^{7}+3q^{11}-q^{17}-q^{19}+\cdots\)
5472.2.a.c 5472.a 1.a $1$ $43.694$ \(\Q\) None \(0\) \(0\) \(-3\) \(3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{5}+3q^{7}-3q^{11}-q^{17}+q^{19}+\cdots\)
5472.2.a.d 5472.a 1.a $1$ $43.694$ \(\Q\) None \(0\) \(0\) \(-3\) \(5\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-3q^{5}+5q^{7}-5q^{11}-4q^{13}+3q^{17}+\cdots\)
5472.2.a.e 5472.a 1.a $1$ $43.694$ \(\Q\) None \(0\) \(0\) \(-2\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-4q^{7}-6q^{11}-4q^{13}+q^{19}+\cdots\)
5472.2.a.f 5472.a 1.a $1$ $43.694$ \(\Q\) None \(0\) \(0\) \(-2\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-4q^{7}-6q^{11}-2q^{13}-6q^{17}+\cdots\)
5472.2.a.g 5472.a 1.a $1$ $43.694$ \(\Q\) None \(0\) \(0\) \(-2\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+4q^{7}+6q^{11}-4q^{13}-q^{19}+\cdots\)
5472.2.a.h 5472.a 1.a $1$ $43.694$ \(\Q\) None \(0\) \(0\) \(-2\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+4q^{7}+6q^{11}-2q^{13}-6q^{17}+\cdots\)
5472.2.a.i 5472.a 1.a $1$ $43.694$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{7}-2q^{11}-q^{13}-3q^{17}-q^{19}+\cdots\)
5472.2.a.j 5472.a 1.a $1$ $43.694$ \(\Q\) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{17}-q^{19}+6q^{23}-5q^{25}-10q^{29}+\cdots\)
5472.2.a.k 5472.a 1.a $1$ $43.694$ \(\Q\) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{17}+q^{19}-6q^{23}-5q^{25}-10q^{29}+\cdots\)
5472.2.a.l 5472.a 1.a $1$ $43.694$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}+2q^{11}-q^{13}-3q^{17}+q^{19}+\cdots\)
5472.2.a.m 5472.a 1.a $1$ $43.694$ \(\Q\) None \(0\) \(0\) \(1\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}-3q^{11}-4q^{13}+3q^{17}+\cdots\)
5472.2.a.n 5472.a 1.a $1$ $43.694$ \(\Q\) None \(0\) \(0\) \(1\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}-3q^{11}+7q^{17}+q^{19}+\cdots\)
5472.2.a.o 5472.a 1.a $1$ $43.694$ \(\Q\) None \(0\) \(0\) \(1\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}+5q^{11}+4q^{13}+3q^{17}+\cdots\)
5472.2.a.p 5472.a 1.a $1$ $43.694$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}-5q^{11}+4q^{13}+3q^{17}+\cdots\)
5472.2.a.q 5472.a 1.a $1$ $43.694$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}+3q^{11}-4q^{13}+3q^{17}+\cdots\)
5472.2.a.r 5472.a 1.a $1$ $43.694$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}+3q^{11}+7q^{17}-q^{19}+\cdots\)
5472.2.a.s 5472.a 1.a $1$ $43.694$ \(\Q\) None \(0\) \(0\) \(2\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-4q^{7}-4q^{11}+2q^{13}-2q^{17}+\cdots\)
5472.2.a.t 5472.a 1.a $1$ $43.694$ \(\Q\) None \(0\) \(0\) \(2\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-4q^{7}+6q^{11}-4q^{13}+q^{19}+\cdots\)
5472.2.a.u 5472.a 1.a $1$ $43.694$ \(\Q\) None \(0\) \(0\) \(2\) \(4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}+4q^{7}-6q^{11}-4q^{13}-q^{19}+\cdots\)
5472.2.a.v 5472.a 1.a $1$ $43.694$ \(\Q\) None \(0\) \(0\) \(2\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+4q^{7}+4q^{11}+2q^{13}-2q^{17}+\cdots\)
5472.2.a.w 5472.a 1.a $2$ $43.694$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}+2\beta q^{11}+(-1+\beta )q^{13}+\cdots\)
5472.2.a.x 5472.a 1.a $2$ $43.694$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}-2\beta q^{11}+(-1+\beta )q^{13}+\cdots\)
5472.2.a.y 5472.a 1.a $2$ $43.694$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+(-1-2\beta )q^{7}+(-2+\beta )q^{11}+\cdots\)
5472.2.a.z 5472.a 1.a $2$ $43.694$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+(-1+2\beta )q^{7}+(2+\beta )q^{11}+\cdots\)
5472.2.a.ba 5472.a 1.a $2$ $43.694$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+(1-2\beta )q^{7}+(-2-\beta )q^{11}+\cdots\)
5472.2.a.bb 5472.a 1.a $2$ $43.694$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+(1+2\beta )q^{7}+(2-\beta )q^{11}+(2+\cdots)q^{13}+\cdots\)
5472.2.a.bc 5472.a 1.a $2$ $43.694$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(1\) \(-6\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-3q^{7}+(-2+\beta )q^{11}+(1-\beta )q^{13}+\cdots\)
5472.2.a.bd 5472.a 1.a $2$ $43.694$ \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(1\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-\beta q^{7}+(-4+\beta )q^{11}-4q^{13}+\cdots\)
5472.2.a.be 5472.a 1.a $2$ $43.694$ \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(1\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+\beta q^{7}+(4-\beta )q^{11}-4q^{13}+\cdots\)
5472.2.a.bf 5472.a 1.a $2$ $43.694$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(1\) \(6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+3q^{7}+(2-\beta )q^{11}+(1-\beta )q^{13}+\cdots\)
5472.2.a.bg 5472.a 1.a $2$ $43.694$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}-2\beta q^{11}+(-1+\beta )q^{13}+\cdots\)
5472.2.a.bh 5472.a 1.a $2$ $43.694$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+2\beta q^{11}+(-1+\beta )q^{13}+\cdots\)
5472.2.a.bi 5472.a 1.a $2$ $43.694$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(3\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+(-1+\beta )q^{7}+(1-\beta )q^{11}+\cdots\)
5472.2.a.bj 5472.a 1.a $2$ $43.694$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(3\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+(-1+\beta )q^{7}+(1+\beta )q^{11}+\cdots\)
5472.2.a.bk 5472.a 1.a $2$ $43.694$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(3\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+(1-\beta )q^{7}+(-1-\beta )q^{11}+\cdots\)
5472.2.a.bl 5472.a 1.a $2$ $43.694$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(3\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+(1-\beta )q^{7}+(-1+\beta )q^{11}+\cdots\)
5472.2.a.bm 5472.a 1.a $3$ $43.694$ 3.3.229.1 None \(0\) \(0\) \(-5\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-2-\beta _{2})q^{5}+\beta _{1}q^{7}-\beta _{1}q^{11}+\cdots\)
5472.2.a.bn 5472.a 1.a $3$ $43.694$ 3.3.229.1 None \(0\) \(0\) \(-5\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-2-\beta _{2})q^{5}-\beta _{1}q^{7}+\beta _{1}q^{11}+\cdots\)
5472.2.a.bo 5472.a 1.a $3$ $43.694$ 3.3.469.1 None \(0\) \(0\) \(3\) \(-5\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{5}+(-2+\beta _{2})q^{7}+(-2+\cdots)q^{11}+\cdots\)
5472.2.a.bp 5472.a 1.a $3$ $43.694$ 3.3.469.1 None \(0\) \(0\) \(3\) \(5\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{5}+(2-\beta _{2})q^{7}+(2+\beta _{2})q^{11}+\cdots\)
5472.2.a.bq 5472.a 1.a $4$ $43.694$ 4.4.19664.1 None \(0\) \(0\) \(-4\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{3})q^{5}+(-1-\beta _{2})q^{7}+(1+\cdots)q^{11}+\cdots\)
5472.2.a.br 5472.a 1.a $4$ $43.694$ 4.4.19664.1 None \(0\) \(0\) \(-4\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{3})q^{5}+(1+\beta _{2})q^{7}+(-1+\cdots)q^{11}+\cdots\)
5472.2.a.bs 5472.a 1.a $4$ $43.694$ 4.4.15317.1 None \(0\) \(0\) \(-1\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}+\beta _{2})q^{5}+\beta _{3}q^{7}+(-2+\beta _{1}+\cdots)q^{11}+\cdots\)
5472.2.a.bt 5472.a 1.a $4$ $43.694$ 4.4.15317.1 None \(0\) \(0\) \(-1\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}+\beta _{2})q^{5}-\beta _{3}q^{7}+(2-\beta _{1}+\cdots)q^{11}+\cdots\)
5472.2.a.bu 5472.a 1.a $4$ $43.694$ 4.4.19664.1 None \(0\) \(0\) \(4\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{3})q^{5}+(-1-\beta _{2})q^{7}+(-1+\cdots)q^{11}+\cdots\)
5472.2.a.bv 5472.a 1.a $4$ $43.694$ 4.4.19664.1 None \(0\) \(0\) \(4\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{3})q^{5}+(1+\beta _{2})q^{7}+(1+\beta _{3})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5472))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5472)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(171))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(228))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(304))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(342))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(456))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(608))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(684))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(912))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1368))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1824))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2736))\)\(^{\oplus 2}\)