Properties

Label 4719.2.a
Level $4719$
Weight $2$
Character orbit 4719.a
Rep. character $\chi_{4719}(1,\cdot)$
Character field $\Q$
Dimension $218$
Newform subspaces $44$
Sturm bound $1232$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 4719 = 3 \cdot 11^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4719.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 44 \)
Sturm bound: \(1232\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4719))\).

Total New Old
Modular forms 640 218 422
Cusp forms 593 218 375
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.

\(3\)\(11\)\(13\)FrickeDim
\(+\)\(+\)\(+\)$+$\(25\)
\(+\)\(+\)\(-\)$-$\(29\)
\(+\)\(-\)\(+\)$-$\(30\)
\(+\)\(-\)\(-\)$+$\(25\)
\(-\)\(+\)\(+\)$-$\(33\)
\(-\)\(+\)\(-\)$+$\(21\)
\(-\)\(-\)\(+\)$+$\(20\)
\(-\)\(-\)\(-\)$-$\(35\)
Plus space\(+\)\(91\)
Minus space\(-\)\(127\)

Trace form

\( 218 q + 4 q^{2} + 218 q^{4} + 4 q^{5} - 2 q^{6} + 12 q^{7} + 218 q^{9} + O(q^{10}) \) \( 218 q + 4 q^{2} + 218 q^{4} + 4 q^{5} - 2 q^{6} + 12 q^{7} + 218 q^{9} - 8 q^{10} + 4 q^{12} + 2 q^{13} - 4 q^{14} + 222 q^{16} + 4 q^{17} + 4 q^{18} - 4 q^{19} + 4 q^{20} + 4 q^{21} + 16 q^{23} - 6 q^{24} + 238 q^{25} + 12 q^{28} + 4 q^{29} - 4 q^{30} - 20 q^{31} + 4 q^{32} - 24 q^{34} - 32 q^{35} + 218 q^{36} + 28 q^{37} - 4 q^{38} + 4 q^{39} - 20 q^{41} + 12 q^{42} + 4 q^{45} + 32 q^{46} - 4 q^{47} - 8 q^{48} + 250 q^{49} + 44 q^{50} + 10 q^{52} + 20 q^{53} - 2 q^{54} - 4 q^{56} + 20 q^{57} + 8 q^{58} - 28 q^{59} + 20 q^{61} - 36 q^{62} + 12 q^{63} + 250 q^{64} - 4 q^{65} - 20 q^{67} + 44 q^{68} - 8 q^{69} + 32 q^{70} - 20 q^{71} + 12 q^{73} + 56 q^{74} + 8 q^{75} - 36 q^{76} - 2 q^{78} - 16 q^{79} + 116 q^{80} + 218 q^{81} + 88 q^{82} - 28 q^{83} + 44 q^{84} + 48 q^{85} + 64 q^{86} + 36 q^{89} - 8 q^{90} - 4 q^{91} + 88 q^{92} + 20 q^{93} + 52 q^{94} - 64 q^{95} - 34 q^{96} + 20 q^{97} + 20 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4719))\) 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 11 13
4719.2.a.a 4719.a 1.a $1$ $37.681$ \(\Q\) None \(-2\) \(-1\) \(0\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}+2q^{6}+3q^{7}+\cdots\)
4719.2.a.b 4719.a 1.a $1$ $37.681$ \(\Q\) None \(-2\) \(1\) \(-2\) \(-3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}-2q^{5}-2q^{6}+\cdots\)
4719.2.a.c 4719.a 1.a $1$ $37.681$ \(\Q\) None \(-1\) \(-1\) \(2\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+2q^{5}+q^{6}+4q^{7}+\cdots\)
4719.2.a.d 4719.a 1.a $1$ $37.681$ \(\Q\) None \(0\) \(-1\) \(2\) \(-5\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+2q^{5}-5q^{7}+q^{9}+2q^{12}+\cdots\)
4719.2.a.e 4719.a 1.a $1$ $37.681$ \(\Q\) None \(0\) \(-1\) \(2\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+2q^{5}-3q^{7}+q^{9}+2q^{12}+\cdots\)
4719.2.a.f 4719.a 1.a $1$ $37.681$ \(\Q\) None \(0\) \(-1\) \(2\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+2q^{5}+3q^{7}+q^{9}+2q^{12}+\cdots\)
4719.2.a.g 4719.a 1.a $1$ $37.681$ \(\Q\) None \(0\) \(-1\) \(2\) \(5\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+2q^{5}+5q^{7}+q^{9}+2q^{12}+\cdots\)
4719.2.a.h 4719.a 1.a $1$ $37.681$ \(\Q\) None \(0\) \(1\) \(0\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-q^{7}+q^{9}-2q^{12}+q^{13}+\cdots\)
4719.2.a.i 4719.a 1.a $1$ $37.681$ \(\Q\) None \(0\) \(1\) \(0\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}+q^{7}+q^{9}-2q^{12}-q^{13}+\cdots\)
4719.2.a.j 4719.a 1.a $1$ $37.681$ \(\Q\) None \(1\) \(-1\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{6}-3q^{8}+q^{9}+\cdots\)
4719.2.a.k 4719.a 1.a $1$ $37.681$ \(\Q\) None \(1\) \(1\) \(-2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}-2q^{5}+q^{6}-3q^{8}+\cdots\)
4719.2.a.l 4719.a 1.a $1$ $37.681$ \(\Q\) None \(2\) \(-1\) \(0\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}-2q^{6}-3q^{7}+\cdots\)
4719.2.a.m 4719.a 1.a $1$ $37.681$ \(\Q\) None \(2\) \(1\) \(-2\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}-2q^{5}+2q^{6}+\cdots\)
4719.2.a.n 4719.a 1.a $2$ $37.681$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-2\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+q^{4}+(-1+\beta )q^{5}-\beta q^{6}+\cdots\)
4719.2.a.o 4719.a 1.a $2$ $37.681$ \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(-4\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}+(-2+\cdots)q^{5}+\cdots\)
4719.2.a.p 4719.a 1.a $2$ $37.681$ \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}+2\beta q^{5}+\cdots\)
4719.2.a.q 4719.a 1.a $3$ $37.681$ 3.3.148.1 None \(-3\) \(3\) \(4\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
4719.2.a.r 4719.a 1.a $3$ $37.681$ 3.3.321.1 None \(-2\) \(-3\) \(-5\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}-q^{3}+(3-\beta _{1})q^{4}+\cdots\)
4719.2.a.s 4719.a 1.a $3$ $37.681$ 3.3.169.1 None \(-2\) \(3\) \(3\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
4719.2.a.t 4719.a 1.a $3$ $37.681$ 3.3.148.1 None \(-1\) \(3\) \(0\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{2}q^{5}+\cdots\)
4719.2.a.u 4719.a 1.a $3$ $37.681$ 3.3.564.1 None \(1\) \(-3\) \(-2\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
4719.2.a.v 4719.a 1.a $3$ $37.681$ 3.3.321.1 None \(2\) \(-3\) \(-5\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{2}-q^{3}+(3-\beta _{1})q^{4}+(-1+\cdots)q^{5}+\cdots\)
4719.2.a.w 4719.a 1.a $3$ $37.681$ 3.3.169.1 None \(2\) \(3\) \(3\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
4719.2.a.x 4719.a 1.a $4$ $37.681$ 4.4.2777.1 None \(-2\) \(-4\) \(-3\) \(5\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{3})q^{2}-q^{3}+(1-\beta _{2}-\beta _{3})q^{4}+\cdots\)
4719.2.a.y 4719.a 1.a $4$ $37.681$ 4.4.2777.1 None \(2\) \(-4\) \(-3\) \(-5\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{3})q^{2}-q^{3}+(1-\beta _{2}-\beta _{3})q^{4}+\cdots\)
4719.2.a.z 4719.a 1.a $4$ $37.681$ 4.4.8468.1 None \(2\) \(-4\) \(0\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}-q^{3}+(2-\beta _{1})q^{4}+\beta _{3}q^{5}+\cdots\)
4719.2.a.ba 4719.a 1.a $5$ $37.681$ 5.5.210557.1 None \(-2\) \(5\) \(3\) \(-6\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}+q^{3}+(1-\beta _{4})q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots\)
4719.2.a.bb 4719.a 1.a $5$ $37.681$ 5.5.394064.1 None \(-1\) \(-5\) \(2\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)
4719.2.a.bc 4719.a 1.a $5$ $37.681$ 5.5.303952.1 None \(-1\) \(5\) \(-2\) \(-6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2}-\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots\)
4719.2.a.bd 4719.a 1.a $5$ $37.681$ 5.5.394064.1 None \(1\) \(-5\) \(2\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)
4719.2.a.be 4719.a 1.a $5$ $37.681$ 5.5.303952.1 None \(1\) \(5\) \(-2\) \(6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2}-\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots\)
4719.2.a.bf 4719.a 1.a $5$ $37.681$ 5.5.210557.1 None \(2\) \(5\) \(3\) \(6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{2}+q^{3}+(1-\beta _{4})q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots\)
4719.2.a.bg 4719.a 1.a $6$ $37.681$ 6.6.966125.1 None \(-1\) \(6\) \(-6\) \(-5\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(-1+\beta _{3}-\beta _{4}+\beta _{5})q^{4}+\cdots\)
4719.2.a.bh 4719.a 1.a $6$ $37.681$ 6.6.966125.1 None \(1\) \(6\) \(-6\) \(5\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(-1+\beta _{3}-\beta _{4}+\beta _{5})q^{4}+\cdots\)
4719.2.a.bi 4719.a 1.a $10$ $37.681$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-3\) \(-10\) \(-8\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{5}+\beta _{6})q^{4}+(-1+\cdots)q^{5}+\cdots\)
4719.2.a.bj 4719.a 1.a $10$ $37.681$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-2\) \(-10\) \(4\) \(4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\)
4719.2.a.bk 4719.a 1.a $10$ $37.681$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-2\) \(10\) \(-4\) \(-12\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots\)
4719.2.a.bl 4719.a 1.a $10$ $37.681$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(2\) \(-10\) \(4\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\)
4719.2.a.bm 4719.a 1.a $10$ $37.681$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(2\) \(10\) \(-4\) \(12\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots\)
4719.2.a.bn 4719.a 1.a $10$ $37.681$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(3\) \(-10\) \(-8\) \(1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{5}+\beta _{6})q^{4}+(-1+\cdots)q^{5}+\cdots\)
4719.2.a.bo 4719.a 1.a $14$ $37.681$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-3\) \(-14\) \(8\) \(-3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{9}+\cdots)q^{5}+\cdots\)
4719.2.a.bp 4719.a 1.a $14$ $37.681$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(3\) \(-14\) \(8\) \(3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{9}+\cdots)q^{5}+\cdots\)
4719.2.a.bq 4719.a 1.a $18$ $37.681$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-1\) \(18\) \(10\) \(-7\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1-\beta _{7}+\cdots)q^{5}+\cdots\)
4719.2.a.br 4719.a 1.a $18$ $37.681$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(1\) \(18\) \(10\) \(7\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1-\beta _{7}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4719))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4719)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(429))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1573))\)\(^{\oplus 2}\)