Properties

Label 1148.2.i
Level $1148$
Weight $2$
Character orbit 1148.i
Rep. character $\chi_{1148}(165,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $52$
Newform subspaces $5$
Sturm bound $336$
Trace bound $7$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 5 \)
Sturm bound: \(336\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1148, [\chi])\).

Total New Old
Modular forms 348 52 296
Cusp forms 324 52 272
Eisenstein series 24 0 24

Trace form

\( 52q + 2q^{3} + 2q^{5} + 8q^{7} - 28q^{9} + O(q^{10}) \) \( 52q + 2q^{3} + 2q^{5} + 8q^{7} - 28q^{9} - 2q^{11} - 8q^{13} + 2q^{19} + 4q^{23} - 24q^{25} + 8q^{27} + 16q^{29} - 18q^{31} - 12q^{33} - 26q^{35} - 8q^{37} - 6q^{39} - 16q^{41} + 24q^{43} + 2q^{45} - 10q^{47} - 8q^{51} - 12q^{53} + 64q^{55} + 2q^{59} + 14q^{61} - 38q^{63} - 4q^{65} - 10q^{67} + 24q^{69} - 16q^{71} - 16q^{73} + 54q^{75} - 24q^{77} - 36q^{79} - 18q^{81} - 16q^{83} + 36q^{85} + 10q^{87} + 32q^{89} - 38q^{91} - 34q^{93} + 18q^{95} + 12q^{97} - 56q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1148, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1148.2.i.a \(2\) \(9.167\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(3\) \(5\) \(q+(-1+\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
1148.2.i.b \(2\) \(9.167\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(1\) \(-4\) \(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-1-2\zeta_{6})q^{7}+\cdots\)
1148.2.i.c \(2\) \(9.167\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(1\) \(4\) \(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
1148.2.i.d \(16\) \(9.167\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+\beta _{14}q^{5}+(-\beta _{5}+\beta _{8})q^{7}+\cdots\)
1148.2.i.e \(30\) \(9.167\) None \(0\) \(1\) \(-3\) \(3\)

Decomposition of \(S_{2}^{\mathrm{old}}(1148, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1148, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(287, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(574, [\chi])\)\(^{\oplus 2}\)