Properties

Label 1148.2.n
Level $1148$
Weight $2$
Character orbit 1148.n
Rep. character $\chi_{1148}(57,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $80$
Newform subspaces $5$
Sturm bound $336$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.n (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 41 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 5 \)
Sturm bound: \(336\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 696 80 616
Cusp forms 648 80 568
Eisenstein series 48 0 48

Trace form

\( 80q + 4q^{3} + 4q^{5} + 68q^{9} + O(q^{10}) \) \( 80q + 4q^{3} + 4q^{5} + 68q^{9} - 10q^{11} + 12q^{15} + 14q^{17} - 26q^{19} + 4q^{21} + 12q^{23} + 12q^{25} + 4q^{27} - 4q^{29} + 2q^{31} - 26q^{33} - 4q^{35} - 10q^{37} + 12q^{39} + 50q^{41} - 6q^{43} + 44q^{45} + 28q^{47} - 20q^{49} + 40q^{51} + 12q^{53} - 56q^{55} - 16q^{57} + 60q^{59} - 12q^{61} - 8q^{63} - 6q^{65} - 26q^{67} - 4q^{69} - 36q^{71} - 40q^{73} - 18q^{75} + 8q^{77} - 4q^{79} + 48q^{81} + 28q^{83} - 140q^{85} + 24q^{87} + 16q^{89} - 8q^{91} - 76q^{93} + 16q^{95} - 56q^{97} + 76q^{99} + O(q^{100}) \)

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.n.a \(8\) \(9.167\) 8.0.64000000.2 None \(0\) \(-4\) \(-2\) \(-2\) \(q+(-\beta _{3}+\beta _{4}+\beta _{6}-\beta _{7})q^{3}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
1148.2.n.b \(8\) \(9.167\) 8.0.64000000.2 None \(0\) \(8\) \(-2\) \(-2\) \(q+(1+\beta _{5})q^{3}+(\beta _{2}+\beta _{7})q^{5}+\beta _{4}q^{7}+\cdots\)
1148.2.n.c \(16\) \(9.167\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-2\) \(-13\) \(4\) \(q+(-\beta _{1}-\beta _{2}+\beta _{5}-\beta _{6})q^{3}+(-1+\cdots)q^{5}+\cdots\)
1148.2.n.d \(24\) \(9.167\) None \(0\) \(-10\) \(4\) \(-6\)
1148.2.n.e \(24\) \(9.167\) None \(0\) \(12\) \(17\) \(6\)

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

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