Properties

Label 1014.2.a
Level $1014$
Weight $2$
Character orbit 1014.a
Rep. character $\chi_{1014}(1,\cdot)$
Character field $\Q$
Dimension $27$
Newform subspaces $15$
Sturm bound $364$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1014.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 15 \)
Sturm bound: \(364\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1014))\).

Total New Old
Modular forms 210 27 183
Cusp forms 155 27 128
Eisenstein series 55 0 55

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

\(2\)\(3\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(1\)
\(+\)\(+\)\(-\)\(-\)\(5\)
\(+\)\(-\)\(+\)\(-\)\(4\)
\(+\)\(-\)\(-\)\(+\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(6\)
Plus space\(+\)\(7\)
Minus space\(-\)\(20\)

Trace form

\( 27 q + q^{2} + q^{3} + 27 q^{4} - 2 q^{5} - q^{6} - 4 q^{7} + q^{8} + 27 q^{9} + O(q^{10}) \) \( 27 q + q^{2} + q^{3} + 27 q^{4} - 2 q^{5} - q^{6} - 4 q^{7} + q^{8} + 27 q^{9} + 2 q^{10} + 4 q^{11} + q^{12} + 8 q^{14} + 2 q^{15} + 27 q^{16} + 2 q^{17} + q^{18} + 8 q^{19} - 2 q^{20} + 4 q^{21} + 8 q^{23} - q^{24} + 37 q^{25} + q^{27} - 4 q^{28} + 6 q^{29} - 2 q^{30} + 4 q^{31} + q^{32} - 4 q^{33} + 2 q^{34} + 27 q^{36} + 2 q^{37} - 4 q^{38} + 2 q^{40} + 10 q^{41} - 4 q^{42} + 4 q^{43} + 4 q^{44} - 2 q^{45} - 8 q^{47} + q^{48} + 31 q^{49} - q^{50} + 10 q^{51} + 22 q^{53} - q^{54} + 16 q^{55} + 8 q^{56} - 8 q^{57} + 6 q^{58} - 4 q^{59} + 2 q^{60} + 14 q^{61} - 4 q^{63} + 27 q^{64} + 4 q^{66} + 16 q^{67} + 2 q^{68} + 8 q^{69} + 8 q^{70} + 8 q^{71} + q^{72} - 2 q^{73} - 2 q^{74} - q^{75} + 8 q^{76} + 24 q^{77} + 12 q^{79} - 2 q^{80} + 27 q^{81} - 6 q^{82} - 12 q^{83} + 4 q^{84} - 4 q^{85} + 4 q^{86} + 10 q^{87} - 14 q^{89} + 2 q^{90} + 8 q^{92} - 4 q^{93} + 16 q^{94} + 32 q^{95} - q^{96} - 10 q^{97} + 9 q^{98} + 4 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1014))\) 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 3 13
1014.2.a.a 1014.a 1.a $1$ $8.097$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots\)
1014.2.a.b 1014.a 1.a $1$ $8.097$ \(\Q\) None \(-1\) \(1\) \(-2\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-2q^{7}+\cdots\)
1014.2.a.c 1014.a 1.a $1$ $8.097$ \(\Q\) None \(-1\) \(1\) \(3\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}+2q^{7}+\cdots\)
1014.2.a.d 1014.a 1.a $1$ $8.097$ \(\Q\) None \(1\) \(-1\) \(-2\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-4q^{7}+\cdots\)
1014.2.a.e 1014.a 1.a $1$ $8.097$ \(\Q\) None \(1\) \(-1\) \(1\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+2q^{7}+\cdots\)
1014.2.a.f 1014.a 1.a $1$ $8.097$ \(\Q\) None \(1\) \(1\) \(-3\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}-2q^{7}+\cdots\)
1014.2.a.g 1014.a 1.a $1$ $8.097$ \(\Q\) None \(1\) \(1\) \(2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+2q^{7}+\cdots\)
1014.2.a.h 1014.a 1.a $2$ $8.097$ \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(0\) \(6\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}+(3-\beta )q^{7}+\cdots\)
1014.2.a.i 1014.a 1.a $2$ $8.097$ \(\Q(\sqrt{3}) \) None \(-2\) \(2\) \(-4\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(-2+\beta )q^{5}-q^{6}+\cdots\)
1014.2.a.j 1014.a 1.a $2$ $8.097$ \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(0\) \(-6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+\beta q^{5}-q^{6}+(-3+\cdots)q^{7}+\cdots\)
1014.2.a.k 1014.a 1.a $2$ $8.097$ \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(4\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(2+\beta )q^{5}+q^{6}+\cdots\)
1014.2.a.l 1014.a 1.a $3$ $8.097$ \(\Q(\zeta_{14})^+\) None \(-3\) \(-3\) \(-1\) \(-9\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(1-3\beta _{1}+\beta _{2})q^{5}+\cdots\)
1014.2.a.m 1014.a 1.a $3$ $8.097$ \(\Q(\zeta_{14})^+\) None \(-3\) \(3\) \(3\) \(-3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(1+\beta _{1}+\beta _{2})q^{5}+\cdots\)
1014.2.a.n 1014.a 1.a $3$ $8.097$ \(\Q(\zeta_{14})^+\) None \(3\) \(-3\) \(1\) \(9\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-\beta _{1}-2\beta _{2})q^{5}+\cdots\)
1014.2.a.o 1014.a 1.a $3$ $8.097$ \(\Q(\zeta_{14})^+\) None \(3\) \(3\) \(-3\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-1-\beta _{1}-\beta _{2})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1014))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1014)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(338))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(507))\)\(^{\oplus 2}\)