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

\( 27 q + q^{2} + q^{3} + 27 q^{4} - 2 q^{5} - q^{6} - 4 q^{7} + q^{8} + 27 q^{9} + 2 q^{10} + 4 q^{11} + q^{12} + 8 q^{14} + 2 q^{15} + 27 q^{16} + 2 q^{17} + q^{18} + 8 q^{19} - 2 q^{20} + 4 q^{21}+ \cdots + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1014))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 13
1014.2.a.a 1014.a 1.a $1$ $8.097$ \(\Q\) None 78.2.e.b \(-1\) \(-1\) \(-1\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots\)
1014.2.a.b 1014.a 1.a $1$ $8.097$ \(\Q\) None 78.2.b.a \(-1\) \(1\) \(-2\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-2q^{7}+\cdots\)
1014.2.a.c 1014.a 1.a $1$ $8.097$ \(\Q\) None 78.2.e.a \(-1\) \(1\) \(3\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}+2q^{7}+\cdots\)
1014.2.a.d 1014.a 1.a $1$ $8.097$ \(\Q\) None 78.2.a.a \(1\) \(-1\) \(-2\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-4q^{7}+\cdots\)
1014.2.a.e 1014.a 1.a $1$ $8.097$ \(\Q\) None 78.2.e.b \(1\) \(-1\) \(1\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+2q^{7}+\cdots\)
1014.2.a.f 1014.a 1.a $1$ $8.097$ \(\Q\) None 78.2.e.a \(1\) \(1\) \(-3\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}-2q^{7}+\cdots\)
1014.2.a.g 1014.a 1.a $1$ $8.097$ \(\Q\) None 78.2.b.a \(1\) \(1\) \(2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+2q^{7}+\cdots\)
1014.2.a.h 1014.a 1.a $2$ $8.097$ \(\Q(\sqrt{3}) \) None 78.2.i.b \(-2\) \(-2\) \(0\) \(6\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}+(3-\beta )q^{7}+\cdots\)
1014.2.a.i 1014.a 1.a $2$ $8.097$ \(\Q(\sqrt{3}) \) None 78.2.i.a \(-2\) \(2\) \(-4\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(-2+\beta )q^{5}-q^{6}+\cdots\)
1014.2.a.j 1014.a 1.a $2$ $8.097$ \(\Q(\sqrt{3}) \) None 78.2.i.b \(2\) \(-2\) \(0\) \(-6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+\beta q^{5}-q^{6}+(-3+\cdots)q^{7}+\cdots\)
1014.2.a.k 1014.a 1.a $2$ $8.097$ \(\Q(\sqrt{3}) \) None 78.2.i.a \(2\) \(2\) \(4\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(2+\beta )q^{5}+q^{6}+\cdots\)
1014.2.a.l 1014.a 1.a $3$ $8.097$ \(\Q(\zeta_{14})^+\) None 1014.2.a.l \(-3\) \(-3\) \(-1\) \(-9\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(1-3\beta _{1}+\beta _{2})q^{5}+\cdots\)
1014.2.a.m 1014.a 1.a $3$ $8.097$ \(\Q(\zeta_{14})^+\) None 1014.2.a.m \(-3\) \(3\) \(3\) \(-3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(1+\beta _{1}+\beta _{2})q^{5}+\cdots\)
1014.2.a.n 1014.a 1.a $3$ $8.097$ \(\Q(\zeta_{14})^+\) None 1014.2.a.l \(3\) \(-3\) \(1\) \(9\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-\beta _{1}-2\beta _{2})q^{5}+\cdots\)
1014.2.a.o 1014.a 1.a $3$ $8.097$ \(\Q(\zeta_{14})^+\) None 1014.2.a.m \(3\) \(3\) \(-3\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-1-\beta _{1}-\beta _{2})q^{5}+\cdots\)

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

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