Properties

Label 5544.2.a
Level $5544$
Weight $2$
Character orbit 5544.a
Rep. character $\chi_{5544}(1,\cdot)$
Character field $\Q$
Dimension $74$
Newform subspaces $43$
Sturm bound $2304$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 5544 = 2^{3} \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5544.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 43 \)
Sturm bound: \(2304\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5544))\).

Total New Old
Modular forms 1184 74 1110
Cusp forms 1121 74 1047
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.

\(2\)\(3\)\(7\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(4\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(5\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(2\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(7\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(4\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(6\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(7\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(3\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(2\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(5\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(7\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(5\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(6\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(4\)
Plus space\(+\)\(31\)
Minus space\(-\)\(43\)

Trace form

\( 74 q + 4 q^{5} + O(q^{10}) \) \( 74 q + 4 q^{5} - 6 q^{11} + 4 q^{13} + 4 q^{17} + 4 q^{23} + 74 q^{25} - 4 q^{29} - 4 q^{31} - 12 q^{41} + 8 q^{43} - 16 q^{47} + 74 q^{49} - 4 q^{53} - 8 q^{59} - 4 q^{61} - 16 q^{65} + 12 q^{67} + 12 q^{71} - 4 q^{73} + 4 q^{77} + 8 q^{79} + 16 q^{83} - 16 q^{85} + 32 q^{89} + 20 q^{91} + 64 q^{95} + 8 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5544))\) 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 7 11
5544.2.a.a 5544.a 1.a $1$ $44.269$ \(\Q\) None \(0\) \(0\) \(-3\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{5}-q^{7}+q^{11}-3q^{13}+6q^{17}+\cdots\)
5544.2.a.b 5544.a 1.a $1$ $44.269$ \(\Q\) None \(0\) \(0\) \(-2\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}-q^{11}+6q^{13}-6q^{17}+\cdots\)
5544.2.a.c 5544.a 1.a $1$ $44.269$ \(\Q\) None \(0\) \(0\) \(-2\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}-q^{11}-6q^{13}+2q^{17}+\cdots\)
5544.2.a.d 5544.a 1.a $1$ $44.269$ \(\Q\) None \(0\) \(0\) \(-2\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}+q^{11}-4q^{17}+4q^{19}+\cdots\)
5544.2.a.e 5544.a 1.a $1$ $44.269$ \(\Q\) None \(0\) \(0\) \(-2\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}+q^{11}+4q^{13}-4q^{19}+\cdots\)
5544.2.a.f 5544.a 1.a $1$ $44.269$ \(\Q\) None \(0\) \(0\) \(-2\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}+q^{11}+4q^{13}+6q^{17}+\cdots\)
5544.2.a.g 5544.a 1.a $1$ $44.269$ \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}+q^{11}-5q^{13}+4q^{17}+\cdots\)
5544.2.a.h 5544.a 1.a $1$ $44.269$ \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}+q^{11}+3q^{13}+7q^{19}+\cdots\)
5544.2.a.i 5544.a 1.a $1$ $44.269$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}+q^{11}-q^{13}+2q^{17}+\cdots\)
5544.2.a.j 5544.a 1.a $1$ $44.269$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}+q^{11}+3q^{13}-2q^{17}+\cdots\)
5544.2.a.k 5544.a 1.a $1$ $44.269$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{7}+q^{11}-6q^{13}-2q^{19}-4q^{23}+\cdots\)
5544.2.a.l 5544.a 1.a $1$ $44.269$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}+q^{11}+2q^{13}+8q^{17}-6q^{19}+\cdots\)
5544.2.a.m 5544.a 1.a $1$ $44.269$ \(\Q\) None \(0\) \(0\) \(1\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}-q^{11}+q^{13}+6q^{17}+\cdots\)
5544.2.a.n 5544.a 1.a $1$ $44.269$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}-q^{11}-q^{13}-2q^{17}+\cdots\)
5544.2.a.o 5544.a 1.a $1$ $44.269$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}-q^{11}+2q^{17}-2q^{19}+\cdots\)
5544.2.a.p 5544.a 1.a $1$ $44.269$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}-q^{11}+3q^{13}+2q^{17}+\cdots\)
5544.2.a.q 5544.a 1.a $1$ $44.269$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}+q^{11}-5q^{13}+6q^{17}+\cdots\)
5544.2.a.r 5544.a 1.a $1$ $44.269$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}+q^{11}-3q^{13}-4q^{17}+\cdots\)
5544.2.a.s 5544.a 1.a $1$ $44.269$ \(\Q\) None \(0\) \(0\) \(2\) \(-1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{7}+q^{11}-2q^{13}-2q^{17}+\cdots\)
5544.2.a.t 5544.a 1.a $1$ $44.269$ \(\Q\) None \(0\) \(0\) \(2\) \(1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}-q^{11}+4q^{13}-6q^{17}+\cdots\)
5544.2.a.u 5544.a 1.a $1$ $44.269$ \(\Q\) None \(0\) \(0\) \(2\) \(1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}+q^{11}+2q^{13}+2q^{17}+\cdots\)
5544.2.a.v 5544.a 1.a $1$ $44.269$ \(\Q\) None \(0\) \(0\) \(3\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+3q^{5}-q^{7}-q^{11}-3q^{13}-6q^{17}+\cdots\)
5544.2.a.w 5544.a 1.a $1$ $44.269$ \(\Q\) None \(0\) \(0\) \(3\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{5}+q^{7}-q^{11}-3q^{13}-4q^{17}+\cdots\)
5544.2.a.x 5544.a 1.a $1$ $44.269$ \(\Q\) None \(0\) \(0\) \(3\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{5}+q^{7}-q^{11}-q^{13}+2q^{17}+\cdots\)
5544.2.a.y 5544.a 1.a $1$ $44.269$ \(\Q\) None \(0\) \(0\) \(4\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{5}-q^{7}+q^{11}-2q^{13}+2q^{19}+\cdots\)
5544.2.a.z 5544.a 1.a $2$ $44.269$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-3\) \(-2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}-q^{7}-q^{11}+(1-\beta )q^{13}+\cdots\)
5544.2.a.ba 5544.a 1.a $2$ $44.269$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-3\) \(-2\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}-q^{7}+q^{11}+(1+\beta )q^{13}+\cdots\)
5544.2.a.bb 5544.a 1.a $2$ $44.269$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-3\) \(2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}+q^{7}-q^{11}+(3-\beta )q^{13}+\cdots\)
5544.2.a.bc 5544.a 1.a $2$ $44.269$ \(\Q(\sqrt{41}) \) None \(0\) \(0\) \(-1\) \(-2\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{5}-q^{7}-q^{11}-\beta q^{13}+2q^{17}+\cdots\)
5544.2.a.bd 5544.a 1.a $2$ $44.269$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-1\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{5}-q^{7}+q^{11}+(2-\beta )q^{13}+2\beta q^{17}+\cdots\)
5544.2.a.be 5544.a 1.a $2$ $44.269$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(3\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}-q^{7}-q^{11}+(-1-\beta )q^{13}+\cdots\)
5544.2.a.bf 5544.a 1.a $2$ $44.269$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(3\) \(-2\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}-q^{7}-q^{11}-2\beta q^{13}+\cdots\)
5544.2.a.bg 5544.a 1.a $2$ $44.269$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(3\) \(-2\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}-q^{7}-q^{11}+(-1+3\beta )q^{13}+\cdots\)
5544.2.a.bh 5544.a 1.a $2$ $44.269$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(3\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}-q^{7}+q^{11}+(1-\beta )q^{13}+\cdots\)
5544.2.a.bi 5544.a 1.a $2$ $44.269$ \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(3\) \(2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+q^{7}+q^{11}+(-3+\beta )q^{13}+\cdots\)
5544.2.a.bj 5544.a 1.a $3$ $44.269$ 3.3.229.1 None \(0\) \(0\) \(-1\) \(3\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{5}+q^{7}-q^{11}+(-2+\beta _{1}-\beta _{2})q^{13}+\cdots\)
5544.2.a.bk 5544.a 1.a $3$ $44.269$ 3.3.568.1 None \(0\) \(0\) \(-1\) \(3\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{5}+q^{7}-q^{11}+\beta _{1}q^{13}+(-2+\cdots)q^{17}+\cdots\)
5544.2.a.bl 5544.a 1.a $3$ $44.269$ 3.3.961.1 None \(0\) \(0\) \(-1\) \(3\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{5}+q^{7}+q^{11}+(1+\beta _{2})q^{13}+\cdots\)
5544.2.a.bm 5544.a 1.a $4$ $44.269$ 4.4.11348.1 None \(0\) \(0\) \(-5\) \(-4\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{5}-q^{7}-q^{11}+(1+\beta _{3})q^{13}+\cdots\)
5544.2.a.bn 5544.a 1.a $4$ $44.269$ 4.4.22592.1 None \(0\) \(0\) \(-2\) \(-4\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{5}-q^{7}-q^{11}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{13}+\cdots\)
5544.2.a.bo 5544.a 1.a $4$ $44.269$ 4.4.123040.1 None \(0\) \(0\) \(-2\) \(4\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{5}+q^{7}-q^{11}+(1-\beta _{3})q^{13}+\cdots\)
5544.2.a.bp 5544.a 1.a $4$ $44.269$ 4.4.22592.1 None \(0\) \(0\) \(2\) \(-4\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{5}-q^{7}+q^{11}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{13}+\cdots\)
5544.2.a.bq 5544.a 1.a $4$ $44.269$ 4.4.123040.1 None \(0\) \(0\) \(2\) \(4\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{5}+q^{7}+q^{11}+(1-\beta _{3})q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5544))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5544)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(198))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(252))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(264))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(308))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(396))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(462))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(504))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(616))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(693))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(792))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(924))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1386))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1848))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2772))\)\(^{\oplus 2}\)