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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4719))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 11 13
4719.2.a.a \(1\) \(37.681\) \(\Q\) None \(-2\) \(-1\) \(0\) \(3\) \(+\) \(-\) \(+\) \(q-2q^{2}-q^{3}+2q^{4}+2q^{6}+3q^{7}+\cdots\)
4719.2.a.b \(1\) \(37.681\) \(\Q\) None \(-2\) \(1\) \(-2\) \(-3\) \(-\) \(-\) \(+\) \(q-2q^{2}+q^{3}+2q^{4}-2q^{5}-2q^{6}+\cdots\)
4719.2.a.c \(1\) \(37.681\) \(\Q\) None \(-1\) \(-1\) \(2\) \(4\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}-q^{4}+2q^{5}+q^{6}+4q^{7}+\cdots\)
4719.2.a.d \(1\) \(37.681\) \(\Q\) None \(0\) \(-1\) \(2\) \(-5\) \(+\) \(-\) \(+\) \(q-q^{3}-2q^{4}+2q^{5}-5q^{7}+q^{9}+2q^{12}+\cdots\)
4719.2.a.e \(1\) \(37.681\) \(\Q\) None \(0\) \(-1\) \(2\) \(-3\) \(+\) \(-\) \(-\) \(q-q^{3}-2q^{4}+2q^{5}-3q^{7}+q^{9}+2q^{12}+\cdots\)
4719.2.a.f \(1\) \(37.681\) \(\Q\) None \(0\) \(-1\) \(2\) \(3\) \(+\) \(-\) \(+\) \(q-q^{3}-2q^{4}+2q^{5}+3q^{7}+q^{9}+2q^{12}+\cdots\)
4719.2.a.g \(1\) \(37.681\) \(\Q\) None \(0\) \(-1\) \(2\) \(5\) \(+\) \(-\) \(-\) \(q-q^{3}-2q^{4}+2q^{5}+5q^{7}+q^{9}+2q^{12}+\cdots\)
4719.2.a.h \(1\) \(37.681\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(-\) \(-\) \(-\) \(q+q^{3}-2q^{4}-q^{7}+q^{9}-2q^{12}+q^{13}+\cdots\)
4719.2.a.i \(1\) \(37.681\) \(\Q\) None \(0\) \(1\) \(0\) \(1\) \(-\) \(-\) \(+\) \(q+q^{3}-2q^{4}+q^{7}+q^{9}-2q^{12}-q^{13}+\cdots\)
4719.2.a.j \(1\) \(37.681\) \(\Q\) None \(1\) \(-1\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}-q^{4}-q^{6}-3q^{8}+q^{9}+\cdots\)
4719.2.a.k \(1\) \(37.681\) \(\Q\) None \(1\) \(1\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}-q^{4}-2q^{5}+q^{6}-3q^{8}+\cdots\)
4719.2.a.l \(1\) \(37.681\) \(\Q\) None \(2\) \(-1\) \(0\) \(-3\) \(+\) \(-\) \(-\) \(q+2q^{2}-q^{3}+2q^{4}-2q^{6}-3q^{7}+\cdots\)
4719.2.a.m \(1\) \(37.681\) \(\Q\) None \(2\) \(1\) \(-2\) \(3\) \(-\) \(-\) \(-\) \(q+2q^{2}+q^{3}+2q^{4}-2q^{5}+2q^{6}+\cdots\)
4719.2.a.n \(2\) \(37.681\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-2\) \(4\) \(+\) \(-\) \(-\) \(q+\beta q^{2}-q^{3}+q^{4}+(-1+\beta )q^{5}-\beta q^{6}+\cdots\)
4719.2.a.o \(2\) \(37.681\) \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(-4\) \(4\) \(-\) \(-\) \(-\) \(q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}+(-2+\cdots)q^{5}+\cdots\)
4719.2.a.p \(2\) \(37.681\) \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}+2\beta q^{5}+\cdots\)
4719.2.a.q \(3\) \(37.681\) 3.3.148.1 None \(-3\) \(3\) \(4\) \(2\) \(-\) \(-\) \(-\) \(q+(-1-\beta _{2})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
4719.2.a.r \(3\) \(37.681\) 3.3.321.1 None \(-2\) \(-3\) \(-5\) \(0\) \(+\) \(-\) \(-\) \(q+(-1-\beta _{2})q^{2}-q^{3}+(3-\beta _{1})q^{4}+\cdots\)
4719.2.a.s \(3\) \(37.681\) 3.3.169.1 None \(-2\) \(3\) \(3\) \(4\) \(-\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
4719.2.a.t \(3\) \(37.681\) 3.3.148.1 None \(-1\) \(3\) \(0\) \(2\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{2}q^{5}+\cdots\)
4719.2.a.u \(3\) \(37.681\) 3.3.564.1 None \(1\) \(-3\) \(-2\) \(-2\) \(+\) \(-\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
4719.2.a.v \(3\) \(37.681\) 3.3.321.1 None \(2\) \(-3\) \(-5\) \(0\) \(+\) \(-\) \(+\) \(q+(1+\beta _{2})q^{2}-q^{3}+(3-\beta _{1})q^{4}+(-1+\cdots)q^{5}+\cdots\)
4719.2.a.w \(3\) \(37.681\) 3.3.169.1 None \(2\) \(3\) \(3\) \(-4\) \(-\) \(-\) \(+\) \(q+(1-\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
4719.2.a.x \(4\) \(37.681\) 4.4.2777.1 None \(-2\) \(-4\) \(-3\) \(5\) \(+\) \(-\) \(-\) \(q+(-1+\beta _{3})q^{2}-q^{3}+(1-\beta _{2}-\beta _{3})q^{4}+\cdots\)
4719.2.a.y \(4\) \(37.681\) 4.4.2777.1 None \(2\) \(-4\) \(-3\) \(-5\) \(+\) \(-\) \(+\) \(q+(1-\beta _{3})q^{2}-q^{3}+(1-\beta _{2}-\beta _{3})q^{4}+\cdots\)
4719.2.a.z \(4\) \(37.681\) 4.4.8468.1 None \(2\) \(-4\) \(0\) \(-2\) \(+\) \(-\) \(+\) \(q-\beta _{2}q^{2}-q^{3}+(2-\beta _{1})q^{4}+\beta _{3}q^{5}+\cdots\)
4719.2.a.ba \(5\) \(37.681\) 5.5.210557.1 None \(-2\) \(5\) \(3\) \(-6\) \(-\) \(-\) \(+\) \(q+\beta _{3}q^{2}+q^{3}+(1-\beta _{4})q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots\)
4719.2.a.bb \(5\) \(37.681\) 5.5.394064.1 None \(-1\) \(-5\) \(2\) \(2\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)
4719.2.a.bc \(5\) \(37.681\) 5.5.303952.1 None \(-1\) \(5\) \(-2\) \(-6\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2}-\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots\)
4719.2.a.bd \(5\) \(37.681\) 5.5.394064.1 None \(1\) \(-5\) \(2\) \(-2\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)
4719.2.a.be \(5\) \(37.681\) 5.5.303952.1 None \(1\) \(5\) \(-2\) \(6\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2}-\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots\)
4719.2.a.bf \(5\) \(37.681\) 5.5.210557.1 None \(2\) \(5\) \(3\) \(6\) \(-\) \(-\) \(-\) \(q-\beta _{3}q^{2}+q^{3}+(1-\beta _{4})q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots\)
4719.2.a.bg \(6\) \(37.681\) 6.6.966125.1 None \(-1\) \(6\) \(-6\) \(-5\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(-1+\beta _{3}-\beta _{4}+\beta _{5})q^{4}+\cdots\)
4719.2.a.bh \(6\) \(37.681\) 6.6.966125.1 None \(1\) \(6\) \(-6\) \(5\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{2}+q^{3}+(-1+\beta _{3}-\beta _{4}+\beta _{5})q^{4}+\cdots\)
4719.2.a.bi \(10\) \(37.681\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-3\) \(-10\) \(-8\) \(-1\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{5}+\beta _{6})q^{4}+(-1+\cdots)q^{5}+\cdots\)
4719.2.a.bj \(10\) \(37.681\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-2\) \(-10\) \(4\) \(4\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\)
4719.2.a.bk \(10\) \(37.681\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-2\) \(10\) \(-4\) \(-12\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots\)
4719.2.a.bl \(10\) \(37.681\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(2\) \(-10\) \(4\) \(-4\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\)
4719.2.a.bm \(10\) \(37.681\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(2\) \(10\) \(-4\) \(12\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots\)
4719.2.a.bn \(10\) \(37.681\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(3\) \(-10\) \(-8\) \(1\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{5}+\beta _{6})q^{4}+(-1+\cdots)q^{5}+\cdots\)
4719.2.a.bo \(14\) \(37.681\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-3\) \(-14\) \(8\) \(-3\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{9}+\cdots)q^{5}+\cdots\)
4719.2.a.bp \(14\) \(37.681\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(3\) \(-14\) \(8\) \(3\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{9}+\cdots)q^{5}+\cdots\)
4719.2.a.bq \(18\) \(37.681\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-1\) \(18\) \(10\) \(-7\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1-\beta _{7}+\cdots)q^{5}+\cdots\)
4719.2.a.br \(18\) \(37.681\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(1\) \(18\) \(10\) \(7\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1-\beta _{7}+\cdots)q^{5}+\cdots\)

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

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