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Properties

Label 1156.2.h
Level $1156$
Weight $2$
Character orbit 1156.h
Rep. character $\chi_{1156}(733,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $92$
Newform subspaces $8$
Sturm bound $306$
Trace bound $33$

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Defining parameters

Level: \( N \) \(=\) \( 1156 = 2^{2} \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1156.h (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 8 \)
Sturm bound: \(306\)
Trace bound: \(33\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1156, [\chi])\).

Total New Old
Modular forms 720 92 628
Cusp forms 504 92 412
Eisenstein series 216 0 216

Trace form

\( 92 q - 4 q^{5} + 4 q^{9} + O(q^{10}) \) \( 92 q - 4 q^{5} + 4 q^{9} + 8 q^{11} + 4 q^{15} + 4 q^{19} - 8 q^{23} - 4 q^{25} + 12 q^{27} - 12 q^{29} - 24 q^{31} - 16 q^{35} - 4 q^{37} - 24 q^{39} - 4 q^{41} + 12 q^{43} + 4 q^{45} + 4 q^{49} + 28 q^{53} + 4 q^{57} + 28 q^{59} - 4 q^{61} - 4 q^{63} - 8 q^{65} + 8 q^{67} + 16 q^{69} - 16 q^{71} + 12 q^{73} - 8 q^{75} + 4 q^{77} + 8 q^{79} - 12 q^{83} + 4 q^{87} - 8 q^{91} - 28 q^{93} - 12 q^{95} - 12 q^{97} - 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1156, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1156.2.h.a 1156.h 17.d $4$ $9.231$ \(\Q(\zeta_{8})\) None \(0\) \(-4\) \(0\) \(4\) $\mathrm{SU}(2)[C_{8}]$ \(q+(-1-\zeta_{8})q^{3}+(\zeta_{8}^{2}+\zeta_{8}^{3})q^{5}+(1+\cdots)q^{7}+\cdots\)
1156.2.h.b 1156.h 17.d $4$ $9.231$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+(-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(-1+\zeta_{8})q^{5}+\cdots\)
1156.2.h.c 1156.h 17.d $4$ $9.231$ \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{8}]$ \(q+(1+\zeta_{8})q^{3}+(-\zeta_{8}^{2}-\zeta_{8}^{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1156.2.h.d 1156.h 17.d $8$ $9.231$ \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+\zeta_{16}^{3}q^{3}+2\zeta_{16}^{6}q^{5}+3\zeta_{16}^{7}q^{7}+\cdots\)
1156.2.h.e 1156.h 17.d $16$ $9.231$ 16.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q-\beta _{10}q^{3}-\beta _{8}q^{5}-\beta _{15}q^{7}+(4\beta _{5}+\cdots)q^{9}+\cdots\)
1156.2.h.f 1156.h 17.d $16$ $9.231$ \(\Q(\zeta_{48})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+\zeta_{48}^{15}q^{3}+(-\zeta_{48}^{3}+2\zeta_{48}^{5})q^{5}+\cdots\)
1156.2.h.g 1156.h 17.d $16$ $9.231$ 16.0.\(\cdots\).4 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+\beta _{6}q^{3}+(-\beta _{13}+\beta _{15})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1156.2.h.h 1156.h 17.d $24$ $9.231$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1156, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1156, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(289, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(578, [\chi])\)\(^{\oplus 2}\)