Properties

Label 627.2.a
Level $627$
Weight $2$
Character orbit 627.a
Rep. character $\chi_{627}(1,\cdot)$
Character field $\Q$
Dimension $31$
Newform subspaces $10$
Sturm bound $160$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 627 = 3 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 627.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(160\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(627))\).

Total New Old
Modular forms 84 31 53
Cusp forms 77 31 46
Eisenstein series 7 0 7

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

\(3\)\(11\)\(19\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(5\)
\(+\)\(-\)\(+\)\(-\)\(5\)
\(+\)\(-\)\(-\)\(+\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(+\)\(3\)
\(-\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(-\)\(-\)\(-\)\(4\)
Plus space\(+\)\(12\)
Minus space\(-\)\(19\)

Trace form

\( 31 q + q^{2} - q^{3} + 29 q^{4} + 10 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} + 31 q^{9} + O(q^{10}) \) \( 31 q + q^{2} - q^{3} + 29 q^{4} + 10 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} + 31 q^{9} - 10 q^{10} - q^{11} - 7 q^{12} + 2 q^{13} - 8 q^{14} - 6 q^{15} + 29 q^{16} + 14 q^{17} + q^{18} - q^{19} + 14 q^{20} - 8 q^{21} - 3 q^{22} - 24 q^{23} - 15 q^{24} + 41 q^{25} - 2 q^{26} - q^{27} - 24 q^{28} + 18 q^{29} + 14 q^{30} - 16 q^{31} - 35 q^{32} - q^{33} + 18 q^{34} - 32 q^{35} + 29 q^{36} - 22 q^{37} - 3 q^{38} - 14 q^{39} + 6 q^{40} + 30 q^{41} + 24 q^{42} - 20 q^{43} + 9 q^{44} + 10 q^{45} - 16 q^{46} - 32 q^{47} + q^{48} + 15 q^{49} + 39 q^{50} - 2 q^{51} + 54 q^{52} + 10 q^{53} - 3 q^{54} + 10 q^{55} - q^{57} + 6 q^{58} + 28 q^{59} - 2 q^{60} - 6 q^{61} + 16 q^{62} - 8 q^{63} - 11 q^{64} + 60 q^{65} + 5 q^{66} - 4 q^{67} - 30 q^{68} - 16 q^{69} + 32 q^{70} - 3 q^{72} + 14 q^{73} - 18 q^{74} + q^{75} - 7 q^{76} - 26 q^{78} - 40 q^{79} + 6 q^{80} + 31 q^{81} - 22 q^{82} - 28 q^{83} - 24 q^{84} + 12 q^{85} - 84 q^{86} + 2 q^{87} - 15 q^{88} + 14 q^{89} - 10 q^{90} + 8 q^{91} - 8 q^{93} - 40 q^{94} - 6 q^{95} - 23 q^{96} - 10 q^{97} - 31 q^{98} - q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(627))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 11 19
627.2.a.a 627.a 1.a $1$ $5.007$ \(\Q\) None 627.2.a.a \(0\) \(1\) \(0\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}+2q^{7}+q^{9}+q^{11}-2q^{12}+\cdots\)
627.2.a.b 627.a 1.a $1$ $5.007$ \(\Q\) None 627.2.a.b \(0\) \(1\) \(4\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}+4q^{5}+2q^{7}+q^{9}-q^{11}+\cdots\)
627.2.a.c 627.a 1.a $3$ $5.007$ 3.3.169.1 None 627.2.a.c \(-2\) \(-3\) \(1\) \(-5\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
627.2.a.d 627.a 1.a $3$ $5.007$ \(\Q(\zeta_{14})^+\) None 627.2.a.d \(-2\) \(3\) \(-7\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
627.2.a.e 627.a 1.a $3$ $5.007$ 3.3.321.1 None 627.2.a.e \(-2\) \(3\) \(-3\) \(-7\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
627.2.a.f 627.a 1.a $3$ $5.007$ \(\Q(\zeta_{14})^+\) None 627.2.a.f \(2\) \(-3\) \(-3\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}-q^{3}+(1-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
627.2.a.g 627.a 1.a $3$ $5.007$ 3.3.169.1 None 627.2.a.g \(2\) \(3\) \(5\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
627.2.a.h 627.a 1.a $4$ $5.007$ 4.4.23377.1 None 627.2.a.h \(1\) \(4\) \(3\) \(-5\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
627.2.a.i 627.a 1.a $5$ $5.007$ 5.5.2179633.1 None 627.2.a.i \(1\) \(-5\) \(3\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{4})q^{5}+\cdots\)
627.2.a.j 627.a 1.a $5$ $5.007$ 5.5.1920025.1 None 627.2.a.j \(1\) \(-5\) \(7\) \(7\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(1-\beta _{4})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(627))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(627)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(209))\)\(^{\oplus 2}\)