Properties

Label 1078.2.i
Level $1078$
Weight $2$
Character orbit 1078.i
Rep. character $\chi_{1078}(901,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $80$
Newform subspaces $4$
Sturm bound $336$
Trace bound $9$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1078.i (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
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 368 80 288
Cusp forms 304 80 224
Eisenstein series 64 0 64

Trace form

\( 80 q + 40 q^{4} + 12 q^{5} + 24 q^{9} + O(q^{10}) \) \( 80 q + 40 q^{4} + 12 q^{5} + 24 q^{9} - 12 q^{11} + 24 q^{15} - 40 q^{16} + 16 q^{22} - 16 q^{23} + 56 q^{25} + 36 q^{26} + 12 q^{31} + 24 q^{33} + 48 q^{36} + 24 q^{37} - 12 q^{38} + 12 q^{44} + 108 q^{45} - 24 q^{47} + 28 q^{53} + 12 q^{58} - 60 q^{59} + 12 q^{60} - 80 q^{64} - 48 q^{66} - 28 q^{67} - 24 q^{71} - 60 q^{75} - 12 q^{80} - 16 q^{81} - 28 q^{86} + 8 q^{88} - 96 q^{89} - 32 q^{92} + 76 q^{93} - 144 q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1078.2.i.a \(16\) \(8.608\) \(\Q(\zeta_{48})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{48}q^{2}+(-\zeta_{48}^{2}+\zeta_{48}^{7}-\zeta_{48}^{10}+\cdots)q^{3}+\cdots\)
1078.2.i.b \(16\) \(8.608\) 16.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{2}-\beta _{3})q^{2}+(-\beta _{4}+\beta _{9})q^{3}+\beta _{1}q^{4}+\cdots\)
1078.2.i.c \(16\) \(8.608\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(12\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{3}-\beta _{4}-\beta _{13})q^{3}+\beta _{10}q^{4}+\cdots\)
1078.2.i.d \(32\) \(8.608\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(1078, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(539, [\chi])\)\(^{\oplus 2}\)