Properties

Label 1148.2.r
Level $1148$
Weight $2$
Character orbit 1148.r
Rep. character $\chi_{1148}(81,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $56$
Newform subspaces $1$
Sturm bound $336$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 287 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(336\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 348 56 292
Cusp forms 324 56 268
Eisenstein series 24 0 24

Trace form

\( 56q + 4q^{5} + 32q^{9} + O(q^{10}) \) \( 56q + 4q^{5} + 32q^{9} - 6q^{21} + 2q^{23} - 24q^{25} - 4q^{31} + 10q^{33} + 10q^{37} + 10q^{39} + 20q^{41} + 8q^{43} - 22q^{45} - 4q^{49} + 18q^{51} + 28q^{57} - 16q^{59} + 16q^{61} + 2q^{73} + 34q^{77} - 28q^{81} - 48q^{83} - 2q^{87} - 42q^{91} + O(q^{100}) \)

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.r.a \(56\) \(9.167\) None \(0\) \(0\) \(4\) \(0\)

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

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