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Properties

Label 5746.2.a
Level $5746$
Weight $2$
Character orbit 5746.a
Rep. character $\chi_{5746}(1,\cdot)$
Character field $\Q$
Dimension $208$
Newform subspaces $48$
Sturm bound $1638$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 5746 = 2 \cdot 13^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5746.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 48 \)
Sturm bound: \(1638\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5746))\).

Total New Old
Modular forms 846 208 638
Cusp forms 791 208 583
Eisenstein series 55 0 55

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

\(2\)\(13\)\(17\)FrickeDim
\(+\)\(+\)\(+\)$+$\(25\)
\(+\)\(+\)\(-\)$-$\(27\)
\(+\)\(-\)\(+\)$-$\(26\)
\(+\)\(-\)\(-\)$+$\(26\)
\(-\)\(+\)\(+\)$-$\(32\)
\(-\)\(+\)\(-\)$+$\(20\)
\(-\)\(-\)\(+\)$+$\(20\)
\(-\)\(-\)\(-\)$-$\(32\)
Plus space\(+\)\(91\)
Minus space\(-\)\(117\)

Trace form

\( 208 q - 2 q^{3} + 208 q^{4} - 6 q^{5} - 6 q^{6} + 4 q^{7} + 204 q^{9} + O(q^{10}) \) \( 208 q - 2 q^{3} + 208 q^{4} - 6 q^{5} - 6 q^{6} + 4 q^{7} + 204 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{12} + 4 q^{14} + 208 q^{16} + 2 q^{17} + 12 q^{18} + 24 q^{19} - 6 q^{20} + 8 q^{21} - 2 q^{22} + 16 q^{23} - 6 q^{24} + 212 q^{25} + 4 q^{27} + 4 q^{28} + 22 q^{29} + 16 q^{30} + 4 q^{31} + 44 q^{33} - 2 q^{34} + 40 q^{35} + 204 q^{36} + 14 q^{37} + 8 q^{38} - 2 q^{40} - 4 q^{41} - 16 q^{42} + 20 q^{43} + 2 q^{44} - 14 q^{45} - 16 q^{46} + 8 q^{47} - 2 q^{48} + 216 q^{49} - 20 q^{50} + 2 q^{51} + 28 q^{53} - 12 q^{54} - 8 q^{55} + 4 q^{56} - 8 q^{57} - 22 q^{58} - 12 q^{59} + 18 q^{61} + 4 q^{62} + 36 q^{63} + 208 q^{64} + 12 q^{66} + 4 q^{67} + 2 q^{68} - 24 q^{69} - 24 q^{70} + 8 q^{71} + 12 q^{72} + 16 q^{73} + 18 q^{74} + 58 q^{75} + 24 q^{76} + 24 q^{77} + 24 q^{79} - 6 q^{80} + 228 q^{81} - 12 q^{82} + 44 q^{83} + 8 q^{84} + 2 q^{85} + 12 q^{86} + 40 q^{87} - 2 q^{88} + 16 q^{89} + 14 q^{90} + 16 q^{92} + 8 q^{93} + 8 q^{94} + 16 q^{95} - 6 q^{96} - 4 q^{97} + 8 q^{98} - 6 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5746))\) 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 13 17
5746.2.a.a 5746.a 1.a $1$ $45.882$ \(\Q\) None \(-1\) \(-3\) \(4\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-3q^{3}+q^{4}+4q^{5}+3q^{6}-q^{7}+\cdots\)
5746.2.a.b 5746.a 1.a $1$ $45.882$ \(\Q\) None \(-1\) \(-2\) \(0\) \(4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}+2q^{6}+4q^{7}-q^{8}+\cdots\)
5746.2.a.c 5746.a 1.a $1$ $45.882$ \(\Q\) None \(-1\) \(-1\) \(-4\) \(1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}+q^{7}+\cdots\)
5746.2.a.d 5746.a 1.a $1$ $45.882$ \(\Q\) None \(-1\) \(0\) \(-2\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}-4q^{7}-q^{8}-3q^{9}+\cdots\)
5746.2.a.e 5746.a 1.a $1$ $45.882$ \(\Q\) None \(-1\) \(0\) \(4\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+4q^{5}+2q^{7}-q^{8}-3q^{9}+\cdots\)
5746.2.a.f 5746.a 1.a $1$ $45.882$ \(\Q\) None \(-1\) \(2\) \(-4\) \(4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-4q^{5}-2q^{6}+4q^{7}+\cdots\)
5746.2.a.g 5746.a 1.a $1$ $45.882$ \(\Q\) None \(-1\) \(2\) \(2\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}+2q^{5}-2q^{6}-2q^{7}+\cdots\)
5746.2.a.h 5746.a 1.a $1$ $45.882$ \(\Q\) None \(1\) \(-3\) \(-4\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-3q^{3}+q^{4}-4q^{5}-3q^{6}+q^{7}+\cdots\)
5746.2.a.i 5746.a 1.a $1$ $45.882$ \(\Q\) None \(1\) \(-1\) \(4\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+4q^{5}-q^{6}-q^{7}+\cdots\)
5746.2.a.j 5746.a 1.a $1$ $45.882$ \(\Q\) None \(1\) \(2\) \(-2\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}-2q^{5}+2q^{6}-2q^{7}+\cdots\)
5746.2.a.k 5746.a 1.a $2$ $45.882$ \(\Q(\sqrt{3}) \) None \(-2\) \(2\) \(-4\) \(-6\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta )q^{3}+q^{4}-2q^{5}+(-1+\cdots)q^{6}+\cdots\)
5746.2.a.l 5746.a 1.a $2$ $45.882$ \(\Q(\sqrt{2}) \) None \(2\) \(-4\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-2+\beta )q^{3}+q^{4}+\beta q^{5}+(-2+\cdots)q^{6}+\cdots\)
5746.2.a.m 5746.a 1.a $2$ $45.882$ \(\Q(\sqrt{5}) \) None \(2\) \(2\) \(-4\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta )q^{3}+q^{4}-2q^{5}+(1+\beta )q^{6}+\cdots\)
5746.2.a.n 5746.a 1.a $2$ $45.882$ \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(4\) \(6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta )q^{3}+q^{4}+2q^{5}+(1+\beta )q^{6}+\cdots\)
5746.2.a.o 5746.a 1.a $3$ $45.882$ \(\Q(\zeta_{14})^+\) None \(-3\) \(-4\) \(5\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-\beta _{1})q^{3}+q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
5746.2.a.p 5746.a 1.a $3$ $45.882$ \(\Q(\zeta_{14})^+\) None \(-3\) \(-1\) \(-1\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(\beta _{1}+2\beta _{2})q^{5}+\cdots\)
5746.2.a.q 5746.a 1.a $3$ $45.882$ \(\Q(\zeta_{14})^+\) None \(-3\) \(-1\) \(2\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(1-\beta _{1})q^{5}+\beta _{1}q^{6}+\cdots\)
5746.2.a.r 5746.a 1.a $3$ $45.882$ 3.3.756.1 None \(-3\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots\)
5746.2.a.s 5746.a 1.a $3$ $45.882$ \(\Q(\zeta_{14})^+\) None \(-3\) \(0\) \(1\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-\beta _{1}-\beta _{2})q^{3}+q^{4}-\beta _{2}q^{5}+\cdots\)
5746.2.a.t 5746.a 1.a $3$ $45.882$ 3.3.148.1 None \(-3\) \(0\) \(2\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{2}q^{3}+q^{4}+(1-\beta _{1})q^{5}-\beta _{2}q^{6}+\cdots\)
5746.2.a.u 5746.a 1.a $3$ $45.882$ 3.3.316.1 None \(-3\) \(2\) \(-4\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta _{2})q^{3}+q^{4}+(-1+\beta _{2})q^{5}+\cdots\)
5746.2.a.v 5746.a 1.a $3$ $45.882$ \(\Q(\zeta_{14})^+\) None \(-3\) \(5\) \(3\) \(-3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(2-\beta _{1})q^{3}+q^{4}+(2-\beta _{1}+2\beta _{2})q^{5}+\cdots\)
5746.2.a.w 5746.a 1.a $3$ $45.882$ \(\Q(\zeta_{14})^+\) None \(3\) \(-4\) \(-5\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1-\beta _{1})q^{3}+q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
5746.2.a.x 5746.a 1.a $3$ $45.882$ 3.3.148.1 None \(3\) \(-2\) \(4\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1+\beta _{2})q^{5}+\cdots\)
5746.2.a.y 5746.a 1.a $3$ $45.882$ \(\Q(\zeta_{14})^+\) None \(3\) \(-1\) \(-2\) \(4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}+(-1+\beta _{1})q^{5}+\cdots\)
5746.2.a.z 5746.a 1.a $3$ $45.882$ \(\Q(\zeta_{14})^+\) None \(3\) \(-1\) \(1\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}+(-\beta _{1}-2\beta _{2})q^{5}+\cdots\)
5746.2.a.ba 5746.a 1.a $3$ $45.882$ 3.3.148.1 None \(3\) \(0\) \(-2\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{2}q^{3}+q^{4}+(-1+\beta _{1})q^{5}+\cdots\)
5746.2.a.bb 5746.a 1.a $3$ $45.882$ \(\Q(\zeta_{14})^+\) None \(3\) \(0\) \(-1\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-\beta _{1}-\beta _{2})q^{3}+q^{4}+\beta _{2}q^{5}+\cdots\)
5746.2.a.bc 5746.a 1.a $3$ $45.882$ 3.3.756.1 None \(3\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
5746.2.a.bd 5746.a 1.a $3$ $45.882$ \(\Q(\zeta_{14})^+\) None \(3\) \(5\) \(-3\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(2-\beta _{1})q^{3}+q^{4}+(-2+\beta _{1}+\cdots)q^{5}+\cdots\)
5746.2.a.be 5746.a 1.a $4$ $45.882$ 4.4.33709.1 None \(-4\) \(-1\) \(3\) \(5\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(1-\beta _{1})q^{5}+\beta _{1}q^{6}+\cdots\)
5746.2.a.bf 5746.a 1.a $4$ $45.882$ 4.4.8957.1 None \(-4\) \(-1\) \(5\) \(1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(1+\beta _{1})q^{5}+\beta _{1}q^{6}+\cdots\)
5746.2.a.bg 5746.a 1.a $4$ $45.882$ 4.4.14013.1 None \(-4\) \(5\) \(-1\) \(1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta _{1})q^{3}+q^{4}-\beta _{1}q^{5}+(-1+\cdots)q^{6}+\cdots\)
5746.2.a.bh 5746.a 1.a $4$ $45.882$ 4.4.8957.1 None \(4\) \(-1\) \(-5\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}+(-1-\beta _{1})q^{5}+\cdots\)
5746.2.a.bi 5746.a 1.a $4$ $45.882$ 4.4.33709.1 None \(4\) \(-1\) \(-3\) \(-5\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}+(-1+\beta _{1})q^{5}+\cdots\)
5746.2.a.bj 5746.a 1.a $4$ $45.882$ 4.4.14013.1 None \(4\) \(5\) \(1\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta _{1})q^{3}+q^{4}+\beta _{1}q^{5}+(1+\cdots)q^{6}+\cdots\)
5746.2.a.bk 5746.a 1.a $6$ $45.882$ 6.6.10893337.1 None \(-6\) \(-2\) \(1\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{4}q^{3}+q^{4}+(1-\beta _{1}-\beta _{4}+\cdots)q^{5}+\cdots\)
5746.2.a.bl 5746.a 1.a $6$ $45.882$ 6.6.137223932.1 None \(-6\) \(1\) \(-3\) \(-3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{4}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
5746.2.a.bm 5746.a 1.a $6$ $45.882$ 6.6.10893337.1 None \(6\) \(-2\) \(-1\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{4}q^{3}+q^{4}+(-\beta _{1}+\beta _{4})q^{5}+\cdots\)
5746.2.a.bn 5746.a 1.a $6$ $45.882$ 6.6.137223932.1 None \(6\) \(1\) \(3\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{4}q^{3}+q^{4}+(1-\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
5746.2.a.bo 5746.a 1.a $8$ $45.882$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(-2\) \(4\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{4}q^{3}+q^{4}+(1+\beta _{6})q^{5}-\beta _{4}q^{6}+\cdots\)
5746.2.a.bp 5746.a 1.a $8$ $45.882$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(-2\) \(-4\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{4}q^{3}+q^{4}+(-1-\beta _{6})q^{5}+\cdots\)
5746.2.a.bq 5746.a 1.a $12$ $45.882$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-12\) \(-1\) \(-7\) \(6\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(-1+\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots\)
5746.2.a.br 5746.a 1.a $12$ $45.882$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-12\) \(2\) \(-8\) \(-6\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(-1+\beta _{3})q^{5}+\cdots\)
5746.2.a.bs 5746.a 1.a $12$ $45.882$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(12\) \(-1\) \(7\) \(-6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}+(1-\beta _{2}+\beta _{4}+\cdots)q^{5}+\cdots\)
5746.2.a.bt 5746.a 1.a $12$ $45.882$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(12\) \(2\) \(8\) \(6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{3})q^{5}+\beta _{1}q^{6}+\cdots\)
5746.2.a.bu 5746.a 1.a $15$ $45.882$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-15\) \(0\) \(0\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{11}q^{5}+\beta _{1}q^{6}+\cdots\)
5746.2.a.bv 5746.a 1.a $15$ $45.882$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(15\) \(0\) \(0\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{11}q^{5}-\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5746))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5746)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(221))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(338))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(442))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2873))\)\(^{\oplus 2}\)