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Properties

Label 1014.2.i
Level $1014$
Weight $2$
Character orbit 1014.i
Rep. character $\chi_{1014}(361,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $48$
Newform subspaces $8$
Sturm bound $364$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1014.i (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 8 \)
Sturm bound: \(364\)
Trace bound: \(10\)
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 48 372
Cusp forms 308 48 260
Eisenstein series 112 0 112

Trace form

\( 48 q + 24 q^{4} - 24 q^{9} + O(q^{10}) \) \( 48 q + 24 q^{4} - 24 q^{9} - 4 q^{10} + 24 q^{14} + 12 q^{15} - 24 q^{16} + 12 q^{17} - 4 q^{22} + 16 q^{23} - 72 q^{25} - 20 q^{29} - 4 q^{30} - 12 q^{33} - 24 q^{35} + 24 q^{36} + 12 q^{37} - 8 q^{38} - 8 q^{40} - 48 q^{41} + 4 q^{42} + 8 q^{43} + 36 q^{49} - 24 q^{50} - 32 q^{51} + 24 q^{53} - 8 q^{55} + 12 q^{56} + 12 q^{58} + 48 q^{59} + 20 q^{62} - 48 q^{64} - 24 q^{66} + 48 q^{67} - 12 q^{68} + 4 q^{69} - 24 q^{71} + 8 q^{74} - 8 q^{75} + 32 q^{77} + 72 q^{79} - 24 q^{81} + 8 q^{82} + 12 q^{84} - 36 q^{85} + 4 q^{88} + 24 q^{89} + 8 q^{90} + 32 q^{92} + 24 q^{93} - 8 q^{94} - 8 q^{95} - 24 q^{98} + O(q^{100}) \)

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.i.a 1014.i 13.e $4$ $8.097$ \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}-\zeta_{12}^{2}q^{3}+(1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
1014.2.i.b 1014.i 13.e $4$ $8.097$ \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}-\zeta_{12}^{2}q^{3}+(1+\cdots)q^{4}+\cdots\)
1014.2.i.c 1014.i 13.e $4$ $8.097$ \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}-\zeta_{12}^{2}q^{3}+(1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
1014.2.i.d 1014.i 13.e $4$ $8.097$ \(\Q(\zeta_{12})\) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+\zeta_{12}^{2}q^{3}+(1+\cdots)q^{4}+\cdots\)
1014.2.i.e 1014.i 13.e $4$ $8.097$ \(\Q(\zeta_{12})\) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+\zeta_{12}^{2}q^{3}+(1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
1014.2.i.f 1014.i 13.e $4$ $8.097$ \(\Q(\zeta_{12})\) None \(0\) \(2\) \(0\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+\zeta_{12}^{2}q^{3}+(1+\cdots)q^{4}+\cdots\)
1014.2.i.g 1014.i 13.e $12$ $8.097$ 12.0.\(\cdots\).1 None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{10}q^{2}-\beta _{7}q^{3}+(1-\beta _{7})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
1014.2.i.h 1014.i 13.e $12$ $8.097$ 12.0.\(\cdots\).1 None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{6}q^{2}+(1-\beta _{7})q^{3}+\beta _{7}q^{4}+(2\beta _{2}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1014, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 2}\)