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Properties

Label 6627.2.a
Level $6627$
Weight $2$
Character orbit 6627.a
Rep. character $\chi_{6627}(1,\cdot)$
Character field $\Q$
Dimension $361$
Newform subspaces $35$
Sturm bound $1504$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 6627 = 3 \cdot 47^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6627.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 35 \)
Sturm bound: \(1504\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6627))\).

Total New Old
Modular forms 800 361 439
Cusp forms 705 361 344
Eisenstein series 95 0 95

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

\(3\)\(47\)FrickeDim
\(+\)\(+\)$+$\(88\)
\(+\)\(-\)$-$\(92\)
\(-\)\(+\)$-$\(104\)
\(-\)\(-\)$+$\(77\)
Plus space\(+\)\(165\)
Minus space\(-\)\(196\)

Trace form

\( 361 q + 3 q^{2} + q^{3} + 363 q^{4} + 2 q^{5} - q^{6} + 4 q^{7} + 3 q^{8} + 361 q^{9} + O(q^{10}) \) \( 361 q + 3 q^{2} + q^{3} + 363 q^{4} + 2 q^{5} - q^{6} + 4 q^{7} + 3 q^{8} + 361 q^{9} - 10 q^{10} - 4 q^{11} - q^{12} + 6 q^{13} - 4 q^{14} + 2 q^{15} + 371 q^{16} - 2 q^{17} + 3 q^{18} - 8 q^{19} + 14 q^{20} + 8 q^{21} + 4 q^{22} - 16 q^{23} - 9 q^{24} + 379 q^{25} + 26 q^{26} + q^{27} + 16 q^{28} + 10 q^{29} + 6 q^{30} - 12 q^{31} + 19 q^{32} + 4 q^{33} - 2 q^{34} - 24 q^{35} + 363 q^{36} + 10 q^{37} - 16 q^{38} - 2 q^{39} - 10 q^{40} - 2 q^{41} + 4 q^{42} - 20 q^{44} + 2 q^{45} + 40 q^{46} + 15 q^{48} + 365 q^{49} + q^{50} + 6 q^{51} - 6 q^{52} - 6 q^{53} - q^{54} - 20 q^{55} - 16 q^{56} + 8 q^{57} - 18 q^{58} - 4 q^{59} + 6 q^{60} - 14 q^{61} - 20 q^{62} + 4 q^{63} + 371 q^{64} + 20 q^{65} - 20 q^{66} - 8 q^{67} - 2 q^{68} - 8 q^{69} + 8 q^{70} + 4 q^{71} + 3 q^{72} + 18 q^{73} + 14 q^{74} - 9 q^{75} - 40 q^{76} - 16 q^{77} - 14 q^{78} + 8 q^{79} + 14 q^{80} + 361 q^{81} + 2 q^{82} + 8 q^{83} + 8 q^{84} + 4 q^{85} + 16 q^{86} - 6 q^{87} + 28 q^{88} - 26 q^{89} - 10 q^{90} - 16 q^{91} - 32 q^{92} + 20 q^{93} - 40 q^{95} - 9 q^{96} + 30 q^{97} - 25 q^{98} - 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6627))\) 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 47
6627.2.a.a 6627.a 1.a $1$ $52.917$ \(\Q\) None \(-2\) \(1\) \(3\) \(-3\) $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}+3q^{5}-2q^{6}+\cdots\)
6627.2.a.b 6627.a 1.a $1$ $52.917$ \(\Q\) None \(-1\) \(-1\) \(0\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}+4q^{7}+3q^{8}+\cdots\)
6627.2.a.c 6627.a 1.a $1$ $52.917$ \(\Q\) None \(-1\) \(1\) \(-2\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-2q^{5}-q^{6}+3q^{8}+\cdots\)
6627.2.a.d 6627.a 1.a $1$ $52.917$ \(\Q\) None \(0\) \(-1\) \(-4\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-4q^{5}+q^{9}+6q^{11}+\cdots\)
6627.2.a.e 6627.a 1.a $1$ $52.917$ \(\Q\) None \(0\) \(-1\) \(1\) \(-3\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+q^{5}-3q^{7}+q^{9}+3q^{11}+\cdots\)
6627.2.a.f 6627.a 1.a $1$ $52.917$ \(\Q\) None \(0\) \(-1\) \(4\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+4q^{5}+q^{9}-6q^{11}+\cdots\)
6627.2.a.g 6627.a 1.a $1$ $52.917$ \(\Q\) None \(0\) \(1\) \(-3\) \(1\) $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-3q^{5}+q^{7}+q^{9}+3q^{11}+\cdots\)
6627.2.a.h 6627.a 1.a $1$ $52.917$ \(\Q\) None \(0\) \(1\) \(3\) \(1\) $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}+3q^{5}+q^{7}+q^{9}-3q^{11}+\cdots\)
6627.2.a.i 6627.a 1.a $1$ $52.917$ \(\Q\) None \(2\) \(1\) \(1\) \(-3\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}-3q^{7}+\cdots\)
6627.2.a.j 6627.a 1.a $2$ $52.917$ \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+\beta q^{5}+q^{6}+3q^{8}+\cdots\)
6627.2.a.k 6627.a 1.a $2$ $52.917$ \(\Q(\sqrt{17}) \) None \(-1\) \(-2\) \(-1\) \(1\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+(2+\beta )q^{4}+(-1+\beta )q^{5}+\cdots\)
6627.2.a.l 6627.a 1.a $2$ $52.917$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(-2\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{5}+\beta q^{6}+\cdots\)
6627.2.a.m 6627.a 1.a $2$ $52.917$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(2\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(1-\beta )q^{5}+\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
6627.2.a.n 6627.a 1.a $2$ $52.917$ \(\Q(\sqrt{17}) \) None \(4\) \(-2\) \(0\) \(-6\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}-\beta q^{5}-2q^{6}+\cdots\)
6627.2.a.o 6627.a 1.a $3$ $52.917$ 3.3.321.1 None \(-1\) \(3\) \(-4\) \(-6\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
6627.2.a.p 6627.a 1.a $3$ $52.917$ 3.3.321.1 None \(-1\) \(3\) \(4\) \(-6\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
6627.2.a.q 6627.a 1.a $3$ $52.917$ 3.3.785.1 None \(1\) \(-3\) \(-4\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
6627.2.a.r 6627.a 1.a $3$ $52.917$ 3.3.785.1 None \(1\) \(-3\) \(4\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
6627.2.a.s 6627.a 1.a $4$ $52.917$ \(\Q(\zeta_{16})^+\) None \(-4\) \(-4\) \(0\) \(8\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}-q^{3}+(1+2\beta _{2})q^{4}+\cdots\)
6627.2.a.t 6627.a 1.a $4$ $52.917$ \(\Q(\zeta_{16})^+\) None \(0\) \(-4\) \(-4\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
6627.2.a.u 6627.a 1.a $4$ $52.917$ \(\Q(\zeta_{16})^+\) None \(0\) \(-4\) \(4\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(1+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
6627.2.a.v 6627.a 1.a $4$ $52.917$ 4.4.7232.1 None \(2\) \(-4\) \(-6\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(\beta _{1}-\beta _{3})q^{2}-q^{3}+(1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
6627.2.a.w 6627.a 1.a $4$ $52.917$ 4.4.7232.1 None \(2\) \(-4\) \(6\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(\beta _{1}-\beta _{3})q^{2}-q^{3}+(1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
6627.2.a.x 6627.a 1.a $4$ $52.917$ \(\Q(\zeta_{16})^+\) None \(4\) \(4\) \(0\) \(8\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+2\beta _{1}q^{5}+q^{6}+(2+\cdots)q^{7}+\cdots\)
6627.2.a.y 6627.a 1.a $6$ $52.917$ \(\Q(\zeta_{36})^+\) None \(-6\) \(6\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{2})q^{2}+q^{3}+(1-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
6627.2.a.z 6627.a 1.a $8$ $52.917$ 8.8.\(\cdots\).1 None \(-2\) \(-8\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{4}q^{2}-q^{3}+(1-\beta _{3})q^{4}+(\beta _{2}-\beta _{7})q^{5}+\cdots\)
6627.2.a.ba 6627.a 1.a $12$ $52.917$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(12\) \(0\) \(-20\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{5}q^{2}+q^{3}-\beta _{7}q^{4}+(\beta _{1}+\beta _{4}-\beta _{6}+\cdots)q^{5}+\cdots\)
6627.2.a.bb 6627.a 1.a $16$ $52.917$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(16\) \(0\) \(8\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+q^{3}+(2+\beta _{9})q^{4}-\beta _{4}q^{5}+\cdots\)
6627.2.a.bc 6627.a 1.a $16$ $52.917$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(8\) \(-16\) \(0\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{8})q^{2}-q^{3}+(1+\beta _{8}-\beta _{11}+\cdots)q^{4}+\cdots\)
6627.2.a.bd 6627.a 1.a $32$ $52.917$ None \(-8\) \(-32\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$
6627.2.a.be 6627.a 1.a $40$ $52.917$ None \(8\) \(40\) \(0\) \(32\) $-$ $+$ $\mathrm{SU}(2)$
6627.2.a.bf 6627.a 1.a $44$ $52.917$ None \(-1\) \(44\) \(-21\) \(-1\) $-$ $-$ $\mathrm{SU}(2)$
6627.2.a.bg 6627.a 1.a $44$ $52.917$ None \(-1\) \(44\) \(21\) \(-1\) $-$ $+$ $\mathrm{SU}(2)$
6627.2.a.bh 6627.a 1.a $44$ $52.917$ None \(1\) \(-44\) \(-23\) \(-1\) $+$ $+$ $\mathrm{SU}(2)$
6627.2.a.bi 6627.a 1.a $44$ $52.917$ None \(1\) \(-44\) \(23\) \(-1\) $+$ $-$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6627))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6627)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(47))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(141))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2209))\)\(^{\oplus 2}\)