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Properties

Label 1078.2.c
Level $1078$
Weight $2$
Character orbit 1078.c
Rep. character $\chi_{1078}(1077,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $3$
Sturm bound $336$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1078.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(336\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1078, [\chi])\).

Total New Old
Modular forms 184 40 144
Cusp forms 152 40 112
Eisenstein series 32 0 32

Trace form

\( 40 q - 40 q^{4} - 24 q^{9} + O(q^{10}) \) \( 40 q - 40 q^{4} - 24 q^{9} + 24 q^{15} + 40 q^{16} + 8 q^{22} - 32 q^{23} - 56 q^{25} + 24 q^{36} + 56 q^{53} + 24 q^{58} - 24 q^{60} - 40 q^{64} + 40 q^{67} - 24 q^{71} - 48 q^{78} - 56 q^{81} - 8 q^{86} - 8 q^{88} + 32 q^{92} - 40 q^{93} + 48 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1078, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1078.2.c.a 1078.c 77.b $8$ $8.608$ \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{16}q^{2}+(-\zeta_{16}^{2}-\zeta_{16}^{4})q^{3}-q^{4}+\cdots\)
1078.2.c.b 1078.c 77.b $16$ $8.608$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{9}q^{2}+\beta _{14}q^{3}-q^{4}+(-\beta _{8}+\beta _{11}+\cdots)q^{5}+\cdots\)
1078.2.c.c 1078.c 77.b $16$ $8.608$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}-\beta _{5}q^{3}-q^{4}+(-\beta _{9}+\beta _{11}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1078, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1078, [\chi]) \cong \)