Properties

Label 1148.2.k
Level $1148$
Weight $2$
Character orbit 1148.k
Rep. character $\chi_{1148}(337,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $44$
Newform subspaces $2$
Sturm bound $336$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 41 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(336\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 348 44 304
Cusp forms 324 44 280
Eisenstein series 24 0 24

Trace form

\( 44q - 4q^{3} + O(q^{10}) \) \( 44q - 4q^{3} + 4q^{13} - 8q^{15} - 8q^{17} + 4q^{19} - 8q^{23} - 68q^{25} + 20q^{27} + 4q^{35} + 16q^{37} + 4q^{41} + 32q^{45} + 32q^{47} - 32q^{51} + 20q^{53} + 8q^{55} + 40q^{57} - 8q^{63} - 4q^{65} - 48q^{67} + 28q^{69} - 12q^{71} + 84q^{75} - 20q^{79} - 116q^{81} - 104q^{83} - 64q^{85} - 12q^{89} + 16q^{93} + 24q^{95} + 40q^{97} + 68q^{99} + O(q^{100}) \)

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.k.a \(8\) \(9.167\) 8.0.110166016.2 None \(0\) \(-4\) \(0\) \(0\) \(q+(-1-\beta _{5})q^{3}+(-1+\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots\)
1148.2.k.b \(36\) \(9.167\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(1148, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(82, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(164, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(287, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(574, [\chi])\)\(^{\oplus 2}\)