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Properties

Label 8030.2.a
Level $8030$
Weight $2$
Character orbit 8030.a
Rep. character $\chi_{8030}(1,\cdot)$
Character field $\Q$
Dimension $241$
Newform subspaces $38$
Sturm bound $2664$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8030.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 38 \)
Sturm bound: \(2664\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8030))\).

Total New Old
Modular forms 1340 241 1099
Cusp forms 1325 241 1084
Eisenstein series 15 0 15

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

\(2\)\(5\)\(11\)\(73\)FrickeDim
\(+\)\(+\)\(+\)\(+\)$+$\(12\)
\(+\)\(+\)\(+\)\(-\)$-$\(18\)
\(+\)\(+\)\(-\)\(+\)$-$\(20\)
\(+\)\(+\)\(-\)\(-\)$+$\(11\)
\(+\)\(-\)\(+\)\(+\)$-$\(15\)
\(+\)\(-\)\(+\)\(-\)$+$\(14\)
\(+\)\(-\)\(-\)\(+\)$+$\(13\)
\(+\)\(-\)\(-\)\(-\)$-$\(17\)
\(-\)\(+\)\(+\)\(+\)$-$\(16\)
\(-\)\(+\)\(+\)\(-\)$+$\(15\)
\(-\)\(+\)\(-\)\(+\)$+$\(13\)
\(-\)\(+\)\(-\)\(-\)$-$\(17\)
\(-\)\(-\)\(+\)\(+\)$+$\(12\)
\(-\)\(-\)\(+\)\(-\)$-$\(18\)
\(-\)\(-\)\(-\)\(+\)$-$\(19\)
\(-\)\(-\)\(-\)\(-\)$+$\(11\)
Plus space\(+\)\(101\)
Minus space\(-\)\(140\)

Trace form

\( 241 q + q^{2} + 4 q^{3} + 241 q^{4} - 3 q^{5} - 4 q^{6} + 8 q^{7} + q^{8} + 245 q^{9} + O(q^{10}) \) \( 241 q + q^{2} + 4 q^{3} + 241 q^{4} - 3 q^{5} - 4 q^{6} + 8 q^{7} + q^{8} + 245 q^{9} + q^{10} + q^{11} + 4 q^{12} + 14 q^{13} + 4 q^{15} + 241 q^{16} + 18 q^{17} + 13 q^{18} + 20 q^{19} - 3 q^{20} + 16 q^{21} - 3 q^{22} + 16 q^{23} - 4 q^{24} + 241 q^{25} + 6 q^{26} + 40 q^{27} + 8 q^{28} + 6 q^{29} - 4 q^{30} + 8 q^{31} + q^{32} - 4 q^{33} + 2 q^{34} - 8 q^{35} + 245 q^{36} + 22 q^{37} + 12 q^{38} + 56 q^{39} + q^{40} + 2 q^{41} - 4 q^{43} + q^{44} - 7 q^{45} - 32 q^{46} + 24 q^{47} + 4 q^{48} + 241 q^{49} + q^{50} + 40 q^{51} + 14 q^{52} + 14 q^{53} - 40 q^{54} + q^{55} + 32 q^{57} - 34 q^{58} + 28 q^{59} + 4 q^{60} + 22 q^{61} - 32 q^{62} + 104 q^{63} + 241 q^{64} + 14 q^{65} + 4 q^{66} + 20 q^{67} + 18 q^{68} + 16 q^{69} - 16 q^{70} + 32 q^{71} + 13 q^{72} + q^{73} + 22 q^{74} + 4 q^{75} + 20 q^{76} + 8 q^{77} - 40 q^{78} + 48 q^{79} - 3 q^{80} + 265 q^{81} - 6 q^{82} - 12 q^{83} + 16 q^{84} + 2 q^{85} + 28 q^{86} + 24 q^{87} - 3 q^{88} - 6 q^{89} + 13 q^{90} + 48 q^{91} + 16 q^{92} + 48 q^{93} - 56 q^{94} - 12 q^{95} - 4 q^{96} + 26 q^{97} + 57 q^{98} + 13 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8030))\) 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 5 11 73
8030.2.a.a 8030.a 1.a $1$ $64.120$ \(\Q\) None \(-1\) \(-1\) \(1\) \(-3\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-3q^{7}+\cdots\)
8030.2.a.b 8030.a 1.a $1$ $64.120$ \(\Q\) None \(-1\) \(0\) \(-1\) \(-2\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-2q^{7}-q^{8}-3q^{9}+\cdots\)
8030.2.a.c 8030.a 1.a $1$ $64.120$ \(\Q\) None \(-1\) \(0\) \(1\) \(2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-3q^{9}+\cdots\)
8030.2.a.d 8030.a 1.a $1$ $64.120$ \(\Q\) None \(-1\) \(1\) \(-1\) \(3\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+3q^{7}+\cdots\)
8030.2.a.e 8030.a 1.a $1$ $64.120$ \(\Q\) None \(-1\) \(3\) \(-1\) \(1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}+q^{4}-q^{5}-3q^{6}+q^{7}+\cdots\)
8030.2.a.f 8030.a 1.a $1$ $64.120$ \(\Q\) None \(-1\) \(3\) \(-1\) \(5\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}+q^{4}-q^{5}-3q^{6}+5q^{7}+\cdots\)
8030.2.a.g 8030.a 1.a $1$ $64.120$ \(\Q\) None \(1\) \(-3\) \(-1\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-3q^{3}+q^{4}-q^{5}-3q^{6}+q^{7}+\cdots\)
8030.2.a.h 8030.a 1.a $1$ $64.120$ \(\Q\) None \(1\) \(-2\) \(-1\) \(4\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-q^{5}-2q^{6}+4q^{7}+\cdots\)
8030.2.a.i 8030.a 1.a $1$ $64.120$ \(\Q\) None \(1\) \(0\) \(-1\) \(4\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+4q^{7}+q^{8}-3q^{9}+\cdots\)
8030.2.a.j 8030.a 1.a $1$ $64.120$ \(\Q\) None \(1\) \(1\) \(1\) \(-1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
8030.2.a.k 8030.a 1.a $2$ $64.120$ \(\Q(\sqrt{13}) \) None \(-2\) \(-1\) \(-2\) \(-2\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta q^{3}+q^{4}-q^{5}+\beta q^{6}+(-2+\cdots)q^{7}+\cdots\)
8030.2.a.l 8030.a 1.a $2$ $64.120$ \(\Q(\sqrt{13}) \) None \(-2\) \(1\) \(-2\) \(-3\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}-q^{5}-\beta q^{6}+(-2+\cdots)q^{7}+\cdots\)
8030.2.a.m 8030.a 1.a $2$ $64.120$ \(\Q(\sqrt{13}) \) None \(2\) \(-3\) \(2\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1-\beta )q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
8030.2.a.n 8030.a 1.a $2$ $64.120$ \(\Q(\sqrt{13}) \) None \(2\) \(-3\) \(2\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1-\beta )q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
8030.2.a.o 8030.a 1.a $2$ $64.120$ \(\Q(\sqrt{5}) \) None \(2\) \(-1\) \(-2\) \(2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta q^{3}+q^{4}-q^{5}-\beta q^{6}+(2+\cdots)q^{7}+\cdots\)
8030.2.a.p 8030.a 1.a $2$ $64.120$ \(\Q(\sqrt{13}) \) None \(2\) \(-1\) \(-2\) \(5\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta q^{3}+q^{4}-q^{5}-\beta q^{6}+(2+\cdots)q^{7}+\cdots\)
8030.2.a.q 8030.a 1.a $2$ $64.120$ \(\Q(\sqrt{17}) \) None \(2\) \(1\) \(-2\) \(-5\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}-q^{5}+\beta q^{6}+(-2+\cdots)q^{7}+\cdots\)
8030.2.a.r 8030.a 1.a $3$ $64.120$ 3.3.316.1 None \(-3\) \(-1\) \(-3\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
8030.2.a.s 8030.a 1.a $3$ $64.120$ 3.3.229.1 None \(-3\) \(0\) \(-3\) \(1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
8030.2.a.t 8030.a 1.a $3$ $64.120$ 3.3.229.1 None \(3\) \(-2\) \(3\) \(-4\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1-\beta _{2})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
8030.2.a.u 8030.a 1.a $4$ $64.120$ 4.4.3981.1 None \(4\) \(-1\) \(4\) \(-12\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{3}q^{3}+q^{4}+q^{5}+\beta _{3}q^{6}+\cdots\)
8030.2.a.v 8030.a 1.a $5$ $64.120$ 5.5.216637.1 None \(5\) \(-5\) \(5\) \(-8\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1-\beta _{3})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
8030.2.a.w 8030.a 1.a $6$ $64.120$ 6.6.47685496.1 None \(-6\) \(-1\) \(-6\) \(6\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
8030.2.a.x 8030.a 1.a $6$ $64.120$ 6.6.32730625.1 None \(-6\) \(2\) \(-6\) \(-3\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+q^{4}-q^{5}+\cdots\)
8030.2.a.y 8030.a 1.a $6$ $64.120$ 6.6.80296592.1 None \(6\) \(-3\) \(6\) \(3\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
8030.2.a.z 8030.a 1.a $7$ $64.120$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(-2\) \(7\) \(-3\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
8030.2.a.ba 8030.a 1.a $7$ $64.120$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(2\) \(7\) \(-7\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{2}q^{3}+q^{4}+q^{5}+\beta _{2}q^{6}+\cdots\)
8030.2.a.bb 8030.a 1.a $8$ $64.120$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(-3\) \(-8\) \(-4\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
8030.2.a.bc 8030.a 1.a $11$ $64.120$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-11\) \(-5\) \(11\) \(-1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
8030.2.a.bd 8030.a 1.a $14$ $64.120$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(14\) \(6\) \(-14\) \(4\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
8030.2.a.be 8030.a 1.a $15$ $64.120$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-15\) \(3\) \(15\) \(7\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
8030.2.a.bf 8030.a 1.a $15$ $64.120$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(15\) \(-4\) \(-15\) \(-6\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
8030.2.a.bg 8030.a 1.a $15$ $64.120$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(15\) \(7\) \(-15\) \(3\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
8030.2.a.bh 8030.a 1.a $17$ $64.120$ \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(-17\) \(-1\) \(-17\) \(1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
8030.2.a.bi 8030.a 1.a $17$ $64.120$ \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(-17\) \(7\) \(17\) \(9\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
8030.2.a.bj 8030.a 1.a $18$ $64.120$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-18\) \(-6\) \(-18\) \(-6\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
8030.2.a.bk 8030.a 1.a $18$ $64.120$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(18\) \(6\) \(18\) \(12\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
8030.2.a.bl 8030.a 1.a $19$ $64.120$ \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None \(19\) \(10\) \(19\) \(8\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+q^{5}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8030))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8030)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(73))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(146))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(365))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(730))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(803))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1606))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4015))\)\(^{\oplus 2}\)