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Properties

Label 1014.2.e
Level $1014$
Weight $2$
Character orbit 1014.e
Rep. character $\chi_{1014}(529,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $52$
Newform subspaces $14$
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.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 14 \)
Sturm bound: \(364\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1014, [\chi])\).

Total New Old
Modular forms 420 52 368
Cusp forms 308 52 256
Eisenstein series 112 0 112

Trace form

\( 52 q - 2 q^{2} - 26 q^{4} - 4 q^{5} + 4 q^{8} - 26 q^{9} + O(q^{10}) \) \( 52 q - 2 q^{2} - 26 q^{4} - 4 q^{5} + 4 q^{8} - 26 q^{9} - 2 q^{10} + 8 q^{11} + 8 q^{14} + 4 q^{15} - 26 q^{16} - 2 q^{17} + 4 q^{18} + 2 q^{20} - 8 q^{21} - 12 q^{22} - 8 q^{23} + 72 q^{25} - 18 q^{29} - 4 q^{30} + 16 q^{31} - 2 q^{32} + 4 q^{33} + 4 q^{34} - 26 q^{36} - 18 q^{37} + 8 q^{38} + 4 q^{40} + 2 q^{41} - 4 q^{42} - 8 q^{43} - 16 q^{44} + 2 q^{45} - 16 q^{47} - 46 q^{49} + 32 q^{51} + 20 q^{53} + 8 q^{55} - 4 q^{56} - 8 q^{57} + 6 q^{58} - 8 q^{59} - 8 q^{60} - 30 q^{61} + 4 q^{62} + 52 q^{64} + 8 q^{66} - 8 q^{67} - 2 q^{68} - 20 q^{69} + 16 q^{70} - 8 q^{71} - 2 q^{72} + 52 q^{73} + 18 q^{74} + 8 q^{75} + 56 q^{79} + 2 q^{80} - 26 q^{81} - 6 q^{82} + 4 q^{84} - 14 q^{85} + 8 q^{87} - 12 q^{88} + 20 q^{89} + 4 q^{90} + 16 q^{92} - 16 q^{94} - 8 q^{95} + 12 q^{97} + 6 q^{98} - 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1014, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1014.2.e.a 1014.e 13.c $2$ $8.097$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(-6\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1014.2.e.b 1014.e 13.c $2$ $8.097$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(4\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1014.2.e.c 1014.e 13.c $2$ $8.097$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1014.2.e.d 1014.e 13.c $2$ $8.097$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1014.2.e.e 1014.e 13.c $2$ $8.097$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-4\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1014.2.e.f 1014.e 13.c $2$ $8.097$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1014.2.e.g 1014.e 13.c $4$ $8.097$ \(\Q(\zeta_{12})\) None \(-2\) \(-2\) \(8\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{12})q^{2}+(-1+\zeta_{12})q^{3}+\cdots\)
1014.2.e.h 1014.e 13.c $4$ $8.097$ \(\Q(\zeta_{12})\) None \(-2\) \(2\) \(0\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{12}q^{2}+\zeta_{12}q^{3}+(-1+\zeta_{12})q^{4}+\cdots\)
1014.2.e.i 1014.e 13.c $4$ $8.097$ \(\Q(\zeta_{12})\) None \(2\) \(-2\) \(-8\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{12}q^{2}-\zeta_{12}q^{3}+(-1+\zeta_{12})q^{4}+\cdots\)
1014.2.e.j 1014.e 13.c $4$ $8.097$ \(\Q(\zeta_{12})\) None \(2\) \(2\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{12}q^{2}+\zeta_{12}q^{3}+(-1+\zeta_{12})q^{4}+\cdots\)
1014.2.e.k 1014.e 13.c $6$ $8.097$ 6.0.64827.1 None \(-3\) \(-3\) \(-6\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{5})q^{2}+(-1+\beta _{5})q^{3}-\beta _{5}q^{4}+\cdots\)
1014.2.e.l 1014.e 13.c $6$ $8.097$ 6.0.64827.1 None \(-3\) \(3\) \(2\) \(-9\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{5})q^{2}+(1-\beta _{5})q^{3}-\beta _{5}q^{4}+\cdots\)
1014.2.e.m 1014.e 13.c $6$ $8.097$ 6.0.64827.1 None \(3\) \(-3\) \(6\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{5}q^{2}-\beta _{5}q^{3}+(-1+\beta _{5})q^{4}+(2\beta _{2}+\cdots)q^{5}+\cdots\)
1014.2.e.n 1014.e 13.c $6$ $8.097$ 6.0.64827.1 None \(3\) \(3\) \(-2\) \(9\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{5}q^{2}+\beta _{5}q^{3}+(-1+\beta _{5})q^{4}+(-2\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1014, [\chi])\) into lower level spaces

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