Properties

Label 7267.2.a
Level $7267$
Weight $2$
Character orbit 7267.a
Rep. character $\chi_{7267}(1,\cdot)$
Character field $\Q$
Dimension $542$
Newform subspaces $22$
Sturm bound $1334$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 7267 = 13^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7267.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 22 \)
Sturm bound: \(1334\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7267))\).

Total New Old
Modular forms 680 542 138
Cusp forms 653 542 111
Eisenstein series 27 0 27

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

\(13\)\(43\)FrickeDim
\(+\)\(+\)$+$\(131\)
\(+\)\(-\)$-$\(141\)
\(-\)\(+\)$-$\(141\)
\(-\)\(-\)$+$\(129\)
Plus space\(+\)\(260\)
Minus space\(-\)\(282\)

Trace form

\( 542 q - q^{2} + 2 q^{3} + 545 q^{4} - 2 q^{5} + 4 q^{7} - 3 q^{8} + 538 q^{9} + O(q^{10}) \) \( 542 q - q^{2} + 2 q^{3} + 545 q^{4} - 2 q^{5} + 4 q^{7} - 3 q^{8} + 538 q^{9} + 6 q^{10} - 5 q^{11} + 12 q^{12} + 4 q^{14} + 12 q^{15} + 551 q^{16} - 9 q^{17} - 17 q^{18} + 6 q^{19} - 6 q^{20} + 4 q^{21} - 14 q^{22} - 5 q^{23} - 12 q^{24} + 554 q^{25} + 8 q^{27} + 12 q^{28} - 20 q^{29} + 23 q^{31} - 27 q^{32} + 6 q^{33} + 4 q^{34} + 501 q^{36} - 6 q^{37} - 44 q^{38} + 30 q^{40} - 17 q^{41} - 2 q^{43} - 26 q^{44} + 30 q^{45} - 2 q^{46} + 8 q^{47} + 24 q^{48} + 530 q^{49} - 11 q^{50} + 14 q^{51} - 7 q^{53} + 12 q^{54} + 20 q^{55} - 20 q^{56} + 8 q^{57} - 30 q^{58} + 4 q^{59} + 56 q^{60} - 8 q^{61} + 14 q^{62} + 40 q^{63} + 551 q^{64} + 24 q^{66} + 17 q^{67} + 8 q^{68} - 14 q^{69} + 80 q^{70} + 2 q^{71} + 9 q^{72} - 10 q^{74} - 14 q^{75} + 60 q^{76} - 44 q^{77} - 8 q^{79} - 6 q^{80} + 494 q^{81} - 32 q^{82} - 17 q^{83} + 68 q^{84} - 20 q^{85} + 5 q^{86} - 24 q^{87} - 48 q^{88} - 30 q^{89} + 66 q^{90} - 10 q^{92} + 6 q^{93} - 24 q^{94} - 24 q^{95} + 32 q^{96} + 21 q^{97} - 53 q^{98} - 69 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7267))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 13 43
7267.2.a.a 7267.a 1.a $1$ $58.027$ \(\Q\) None \(2\) \(-2\) \(4\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-2q^{3}+2q^{4}+4q^{5}-4q^{6}+\cdots\)
7267.2.a.b 7267.a 1.a $2$ $58.027$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-4\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+\beta q^{3}+(-2-\beta )q^{5}+2q^{6}+\cdots\)
7267.2.a.c 7267.a 1.a $2$ $58.027$ \(\Q(\sqrt{3}) \) None \(0\) \(4\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{4}-2\beta q^{5}+q^{9}-2\beta q^{11}+\cdots\)
7267.2.a.d 7267.a 1.a $2$ $58.027$ \(\Q(\sqrt{3}) \) None \(0\) \(4\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+2q^{3}+q^{4}+2\beta q^{5}+2\beta q^{6}+\cdots\)
7267.2.a.e 7267.a 1.a $3$ $58.027$ \(\Q(\zeta_{18})^+\) None \(3\) \(0\) \(3\) \(3\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+\beta _{1}q^{3}+(1-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
7267.2.a.f 7267.a 1.a $4$ $58.027$ 4.4.12197.1 None \(1\) \(1\) \(5\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{1}q^{3}+(1+\beta _{2}-\beta _{3})q^{4}+\cdots\)
7267.2.a.g 7267.a 1.a $7$ $58.027$ 7.7.91138133.1 None \(2\) \(-3\) \(0\) \(1\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(\beta _{1}+\beta _{2}+\beta _{5})q^{4}+\cdots\)
7267.2.a.h 7267.a 1.a $8$ $58.027$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(\beta _{1}-\beta _{5})q^{5}+\cdots\)
7267.2.a.i 7267.a 1.a $14$ $58.027$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-7\) \(1\) \(-12\) \(-1\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-\beta _{10}q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
7267.2.a.j 7267.a 1.a $14$ $58.027$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(-6\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{12}q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
7267.2.a.k 7267.a 1.a $15$ $58.027$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-2\) \(1\) \(2\) \(-1\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{10}q^{3}+(1+\beta _{2})q^{4}+\beta _{9}q^{5}+\cdots\)
7267.2.a.l 7267.a 1.a $23$ $58.027$ None \(-1\) \(-6\) \(2\) \(0\) $+$ $+$ $\mathrm{SU}(2)$
7267.2.a.m 7267.a 1.a $23$ $58.027$ None \(1\) \(-6\) \(-2\) \(0\) $+$ $+$ $\mathrm{SU}(2)$
7267.2.a.n 7267.a 1.a $26$ $58.027$ None \(0\) \(6\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$
7267.2.a.o 7267.a 1.a $27$ $58.027$ None \(-1\) \(6\) \(2\) \(0\) $+$ $-$ $\mathrm{SU}(2)$
7267.2.a.p 7267.a 1.a $27$ $58.027$ None \(1\) \(6\) \(-2\) \(0\) $+$ $-$ $\mathrm{SU}(2)$
7267.2.a.q 7267.a 1.a $44$ $58.027$ None \(0\) \(-12\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$
7267.2.a.r 7267.a 1.a $48$ $58.027$ None \(0\) \(4\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$
7267.2.a.s 7267.a 1.a $63$ $58.027$ None \(-15\) \(1\) \(-43\) \(-14\) $+$ $+$ $\mathrm{SU}(2)$
7267.2.a.t 7267.a 1.a $63$ $58.027$ None \(-15\) \(1\) \(-41\) \(-10\) $-$ $-$ $\mathrm{SU}(2)$
7267.2.a.u 7267.a 1.a $63$ $58.027$ None \(15\) \(1\) \(41\) \(10\) $+$ $-$ $\mathrm{SU}(2)$
7267.2.a.v 7267.a 1.a $63$ $58.027$ None \(15\) \(1\) \(43\) \(14\) $-$ $+$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7267))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7267)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(43))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(559))\)\(^{\oplus 2}\)