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Properties

Label 5733.2.a
Level $5733$
Weight $2$
Character orbit 5733.a
Rep. character $\chi_{5733}(1,\cdot)$
Character field $\Q$
Dimension $205$
Newform subspaces $54$
Sturm bound $1568$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 5733 = 3^{2} \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5733.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 54 \)
Sturm bound: \(1568\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(2\), \(5\), \(11\), \(17\), \(19\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5733))\).

Total New Old
Modular forms 816 205 611
Cusp forms 753 205 548
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.

\(3\)\(7\)\(13\)FrickeDim
\(+\)\(+\)\(+\)$+$\(18\)
\(+\)\(+\)\(-\)$-$\(22\)
\(+\)\(-\)\(+\)$-$\(24\)
\(+\)\(-\)\(-\)$+$\(18\)
\(-\)\(+\)\(+\)$-$\(31\)
\(-\)\(+\)\(-\)$+$\(29\)
\(-\)\(-\)\(+\)$+$\(30\)
\(-\)\(-\)\(-\)$-$\(33\)
Plus space\(+\)\(95\)
Minus space\(-\)\(110\)

Trace form

\( 205 q - 3 q^{2} + 199 q^{4} - 2 q^{5} - 15 q^{8} + O(q^{10}) \) \( 205 q - 3 q^{2} + 199 q^{4} - 2 q^{5} - 15 q^{8} - 10 q^{10} - 12 q^{11} - q^{13} + 183 q^{16} - 2 q^{17} - 4 q^{19} - 30 q^{20} + 8 q^{22} - 8 q^{23} + 227 q^{25} + 3 q^{26} - 2 q^{29} - 12 q^{31} - 3 q^{32} + 30 q^{34} + 14 q^{37} - 4 q^{38} + 18 q^{40} + 6 q^{41} - 20 q^{43} - 12 q^{44} - 8 q^{46} - 4 q^{47} + 23 q^{50} - 7 q^{52} - 26 q^{53} - 12 q^{55} + 6 q^{58} - 4 q^{59} - 50 q^{61} + 4 q^{62} + 179 q^{64} - 6 q^{65} - 12 q^{67} - 2 q^{68} - 8 q^{71} + 6 q^{73} - 38 q^{74} + 8 q^{76} - 48 q^{79} - 90 q^{80} + 42 q^{82} + 20 q^{83} - 16 q^{85} + 64 q^{86} + 108 q^{88} + 22 q^{89} + 52 q^{92} + 28 q^{94} + 16 q^{95} + 38 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5733))\) 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 7 13
5733.2.a.a 5733.a 1.a $1$ $45.778$ \(\Q\) None \(-2\) \(0\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+q^{5}-2q^{10}+2q^{11}+\cdots\)
5733.2.a.b 5733.a 1.a $1$ $45.778$ \(\Q\) None \(-1\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+3q^{8}+q^{13}-q^{16}-2q^{17}+\cdots\)
5733.2.a.c 5733.a 1.a $1$ $45.778$ \(\Q\) None \(-1\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+3q^{8}+3q^{11}-q^{13}+\cdots\)
5733.2.a.d 5733.a 1.a $1$ $45.778$ \(\Q\) None \(-1\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+3q^{8}+3q^{11}+q^{13}+\cdots\)
5733.2.a.e 5733.a 1.a $1$ $45.778$ \(\Q\) None \(-1\) \(0\) \(2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+2q^{5}+3q^{8}-2q^{10}+\cdots\)
5733.2.a.f 5733.a 1.a $1$ $45.778$ \(\Q\) None \(0\) \(0\) \(-3\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}-3q^{5}-q^{13}+4q^{16}-6q^{17}+\cdots\)
5733.2.a.g 5733.a 1.a $1$ $45.778$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}-q^{5}+2q^{11}-q^{13}+4q^{16}+\cdots\)
5733.2.a.h 5733.a 1.a $1$ $45.778$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}+q^{5}+2q^{11}+q^{13}+4q^{16}+\cdots\)
5733.2.a.i 5733.a 1.a $1$ $45.778$ \(\Q\) None \(1\) \(0\) \(-4\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-4q^{5}-3q^{8}-4q^{10}+\cdots\)
5733.2.a.j 5733.a 1.a $1$ $45.778$ \(\Q\) None \(1\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-3q^{8}+q^{13}-q^{16}+2q^{17}+\cdots\)
5733.2.a.k 5733.a 1.a $1$ $45.778$ \(\Q\) None \(1\) \(0\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+4q^{5}-3q^{8}+4q^{10}+\cdots\)
5733.2.a.l 5733.a 1.a $1$ $45.778$ \(\Q\) None \(2\) \(0\) \(-3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-3q^{5}-6q^{10}+6q^{11}+\cdots\)
5733.2.a.m 5733.a 1.a $1$ $45.778$ \(\Q\) None \(2\) \(0\) \(-1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-q^{5}-2q^{10}+2q^{11}+\cdots\)
5733.2.a.n 5733.a 1.a $2$ $45.778$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+(-3+\beta )q^{8}+\cdots\)
5733.2.a.o 5733.a 1.a $2$ $45.778$ \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}-\beta q^{5}+2\beta q^{11}-q^{13}+4q^{16}+\cdots\)
5733.2.a.p 5733.a 1.a $2$ $45.778$ \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}-\beta q^{5}-2\beta q^{11}+q^{13}+4q^{16}+\cdots\)
5733.2.a.q 5733.a 1.a $2$ $45.778$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{5}-2\beta q^{8}-\beta q^{10}+2q^{11}+\cdots\)
5733.2.a.r 5733.a 1.a $2$ $45.778$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{5}-2\beta q^{8}+\beta q^{10}+2q^{11}+\cdots\)
5733.2.a.s 5733.a 1.a $2$ $45.778$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(6\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(3-\beta )q^{5}-2\beta q^{8}+(-2+3\beta )q^{10}+\cdots\)
5733.2.a.t 5733.a 1.a $2$ $45.778$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}-\beta q^{8}-2\beta q^{11}-q^{13}+\cdots\)
5733.2.a.u 5733.a 1.a $2$ $45.778$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+2\beta q^{5}+(3+\cdots)q^{8}+\cdots\)
5733.2.a.v 5733.a 1.a $2$ $45.778$ \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+3\beta q^{4}+(1-2\beta )q^{5}+(1+\cdots)q^{8}+\cdots\)
5733.2.a.w 5733.a 1.a $2$ $45.778$ \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+3\beta q^{4}+(-1+2\beta )q^{5}+\cdots\)
5733.2.a.x 5733.a 1.a $3$ $45.778$ 3.3.316.1 None \(-1\) \(0\) \(2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{1})q^{5}+\cdots\)
5733.2.a.y 5733.a 1.a $3$ $45.778$ \(\Q(\zeta_{18})^+\) None \(0\) \(0\) \(-3\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{2}q^{4}+(-1-\beta _{1})q^{5}+(-1+\cdots)q^{8}+\cdots\)
5733.2.a.z 5733.a 1.a $3$ $45.778$ \(\Q(\zeta_{18})^+\) None \(0\) \(0\) \(3\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{2}q^{4}+(1+\beta _{1})q^{5}+(-1+\cdots)q^{8}+\cdots\)
5733.2.a.ba 5733.a 1.a $3$ $45.778$ \(\Q(\zeta_{14})^+\) None \(2\) \(0\) \(-3\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
5733.2.a.bb 5733.a 1.a $3$ $45.778$ \(\Q(\zeta_{14})^+\) None \(2\) \(0\) \(3\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
5733.2.a.bc 5733.a 1.a $3$ $45.778$ 3.3.316.1 None \(2\) \(0\) \(-3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(2-2\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
5733.2.a.bd 5733.a 1.a $3$ $45.778$ 3.3.404.1 None \(2\) \(0\) \(-5\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
5733.2.a.be 5733.a 1.a $3$ $45.778$ 3.3.404.1 None \(2\) \(0\) \(5\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots\)
5733.2.a.bf 5733.a 1.a $4$ $45.778$ 4.4.17428.1 None \(-1\) \(0\) \(-3\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
5733.2.a.bg 5733.a 1.a $4$ $45.778$ 4.4.7168.1 None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)
5733.2.a.bh 5733.a 1.a $4$ $45.778$ 4.4.7168.1 None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)
5733.2.a.bi 5733.a 1.a $4$ $45.778$ \(\Q(\sqrt{3}, \sqrt{11})\) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{3})q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
5733.2.a.bj 5733.a 1.a $4$ $45.778$ 4.4.69777.1 None \(1\) \(0\) \(-3\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1+\beta _{1})q^{5}+\cdots\)
5733.2.a.bk 5733.a 1.a $4$ $45.778$ 4.4.69777.1 None \(1\) \(0\) \(3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1-\beta _{1})q^{5}+\cdots\)
5733.2.a.bl 5733.a 1.a $5$ $45.778$ 5.5.746052.1 None \(-4\) \(0\) \(-2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{3}-\beta _{4})q^{4}+\cdots\)
5733.2.a.bm 5733.a 1.a $5$ $45.778$ 5.5.746052.1 None \(-4\) \(0\) \(2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{3}-\beta _{4})q^{4}+\cdots\)
5733.2.a.bn 5733.a 1.a $5$ $45.778$ 5.5.2196544.1 None \(-2\) \(0\) \(-3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{4})q^{5}+\cdots\)
5733.2.a.bo 5733.a 1.a $5$ $45.778$ 5.5.2196544.1 None \(-2\) \(0\) \(3\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{4})q^{5}+\cdots\)
5733.2.a.bp 5733.a 1.a $5$ $45.778$ 5.5.375116.1 None \(0\) \(0\) \(-3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{2}+(1-\beta _{4})q^{4}+(-1+\beta _{2})q^{5}+\cdots\)
5733.2.a.bq 5733.a 1.a $5$ $45.778$ 5.5.375116.1 None \(0\) \(0\) \(3\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{2}+(1-\beta _{4})q^{4}+(1-\beta _{2})q^{5}+\cdots\)
5733.2.a.br 5733.a 1.a $6$ $45.778$ 6.6.4507648.1 None \(0\) \(0\) \(-6\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+(1-\beta _{1}-\beta _{3}+\beta _{4})q^{4}+(-1+\cdots)q^{5}+\cdots\)
5733.2.a.bs 5733.a 1.a $6$ $45.778$ 6.6.46162368.1 None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\beta _{3}q^{8}+\cdots\)
5733.2.a.bt 5733.a 1.a $6$ $45.778$ 6.6.46162368.1 None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\beta _{3}q^{8}+\cdots\)
5733.2.a.bu 5733.a 1.a $6$ $45.778$ 6.6.4507648.1 None \(0\) \(0\) \(6\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+(1-\beta _{1}-\beta _{3}+\beta _{4})q^{4}+(1+\cdots)q^{5}+\cdots\)
5733.2.a.bv 5733.a 1.a $6$ $45.778$ 6.6.199374400.1 None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{4}q^{2}+(2+\beta _{2})q^{4}+\beta _{3}q^{5}+(2\beta _{4}+\cdots)q^{8}+\cdots\)
5733.2.a.bw 5733.a 1.a $10$ $45.778$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-4\) \(0\) \(-6\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{5})q^{5}+\cdots\)
5733.2.a.bx 5733.a 1.a $10$ $45.778$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-4\) \(0\) \(6\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1+\beta _{5})q^{5}+\cdots\)
5733.2.a.by 5733.a 1.a $10$ $45.778$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{5}q^{5}+(2\beta _{1}+\cdots)q^{8}+\cdots\)
5733.2.a.bz 5733.a 1.a $10$ $45.778$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{5}q^{5}+(2\beta _{1}+\cdots)q^{8}+\cdots\)
5733.2.a.ca 5733.a 1.a $12$ $45.778$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{10}q^{5}+(\beta _{1}+\cdots)q^{8}+\cdots\)
5733.2.a.cb 5733.a 1.a $12$ $45.778$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{10}q^{5}+(\beta _{1}+\cdots)q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5733))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5733)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(273))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(441))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(637))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(819))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1911))\)\(^{\oplus 2}\)