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Properties

Label 1122.2.l
Level $1122$
Weight $2$
Character orbit 1122.l
Rep. character $\chi_{1122}(463,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $64$
Newform subspaces $7$
Sturm bound $432$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 1122 = 2 \cdot 3 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1122.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 7 \)
Sturm bound: \(432\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1122, [\chi])\).

Total New Old
Modular forms 448 64 384
Cusp forms 416 64 352
Eisenstein series 32 0 32

Trace form

\( 64 q - 64 q^{4} - 8 q^{5} + O(q^{10}) \) \( 64 q - 64 q^{4} - 8 q^{5} + 8 q^{10} + 64 q^{16} + 8 q^{17} - 8 q^{18} + 8 q^{20} - 16 q^{23} + 8 q^{29} - 32 q^{31} + 8 q^{33} - 8 q^{34} + 32 q^{35} + 16 q^{37} - 32 q^{38} - 8 q^{40} + 56 q^{41} + 8 q^{45} + 16 q^{46} - 16 q^{47} - 8 q^{50} - 16 q^{58} - 24 q^{61} - 64 q^{64} - 32 q^{65} - 8 q^{68} + 32 q^{69} + 16 q^{71} + 8 q^{72} - 8 q^{73} + 24 q^{74} - 48 q^{75} + 16 q^{78} + 64 q^{79} - 8 q^{80} - 64 q^{81} - 16 q^{82} - 8 q^{85} + 48 q^{89} + 8 q^{90} + 48 q^{91} + 16 q^{92} - 144 q^{95} + 48 q^{97} + 40 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1122, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1122.2.l.a 1122.l 17.c $4$ $8.959$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}+(-1+2\zeta_{8}+\cdots)q^{5}+\cdots\)
1122.2.l.b 1122.l 17.c $4$ $8.959$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}+(-1+2\zeta_{8}+\cdots)q^{5}+\cdots\)
1122.2.l.c 1122.l 17.c $4$ $8.959$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-q^{4}+(1+2\zeta_{8}+\cdots)q^{5}+\cdots\)
1122.2.l.d 1122.l 17.c $4$ $8.959$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}+(2+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
1122.2.l.e 1122.l 17.c $12$ $8.959$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{2}-\beta _{1}q^{3}-q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots\)
1122.2.l.f 1122.l 17.c $16$ $8.959$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{10}q^{2}-\beta _{6}q^{3}-q^{4}+\beta _{15}q^{5}+\cdots\)
1122.2.l.g 1122.l 17.c $20$ $8.959$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{8}q^{2}-\beta _{2}q^{3}-q^{4}+\beta _{6}q^{5}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1122, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1122, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(102, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(187, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(374, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(561, [\chi])\)\(^{\oplus 2}\)