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Properties

Label 1044.2.z
Level $1044$
Weight $2$
Character orbit 1044.z
Rep. character $\chi_{1044}(109,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $72$
Newform subspaces $4$
Sturm bound $360$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1044 = 2^{2} \cdot 3^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1044.z (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 29 \)
Character field: \(\Q(\zeta_{14})\)
Newform subspaces: \( 4 \)
Sturm bound: \(360\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1044, [\chi])\).

Total New Old
Modular forms 1152 72 1080
Cusp forms 1008 72 936
Eisenstein series 144 0 144

Trace form

\( 72 q + 2 q^{5} - 4 q^{7} + O(q^{10}) \) \( 72 q + 2 q^{5} - 4 q^{7} - 12 q^{13} - 28 q^{23} - 6 q^{25} - 6 q^{29} - 14 q^{31} - 42 q^{35} + 14 q^{37} - 14 q^{43} + 28 q^{47} - 50 q^{49} - 2 q^{53} + 56 q^{55} + 52 q^{59} - 56 q^{61} + 28 q^{65} - 30 q^{67} + 20 q^{71} + 14 q^{73} + 42 q^{77} + 14 q^{79} - 4 q^{83} + 14 q^{85} + 84 q^{89} + 64 q^{91} - 28 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1044, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1044.2.z.a 1044.z 29.e $6$ $8.336$ \(\Q(\zeta_{14})\) None 116.2.i.b \(0\) \(0\) \(1\) \(-5\) $\mathrm{SU}(2)[C_{14}]$ \(q+(-1+2\zeta_{14}-\zeta_{14}^{2}-2\zeta_{14}^{4}+2\zeta_{14}^{5})q^{5}+\cdots\)
1044.2.z.b 1044.z 29.e $6$ $8.336$ \(\Q(\zeta_{14})\) None 116.2.i.a \(0\) \(0\) \(1\) \(9\) $\mathrm{SU}(2)[C_{14}]$ \(q+(1+\zeta_{14}^{2}+2\zeta_{14}^{4}-2\zeta_{14}^{5})q^{5}+\cdots\)
1044.2.z.c 1044.z 29.e $24$ $8.336$ None 1044.2.z.c \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{14}]$
1044.2.z.d 1044.z 29.e $36$ $8.336$ None 348.2.n.a \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{14}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1044, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1044, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(58, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(87, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(116, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(174, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(261, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(348, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(522, [\chi])\)\(^{\oplus 2}\)