Properties

Label 152.7.e
Level $152$
Weight $7$
Character orbit 152.e
Rep. character $\chi_{152}(113,\cdot)$
Character field $\Q$
Dimension $30$
Newform subspaces $1$
Sturm bound $140$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 152 = 2^{3} \cdot 19 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 152.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(140\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(152, [\chi])\).

Total New Old
Modular forms 124 30 94
Cusp forms 116 30 86
Eisenstein series 8 0 8

Trace form

\( 30q - 720q^{7} - 8670q^{9} + O(q^{10}) \) \( 30q - 720q^{7} - 8670q^{9} - 2524q^{11} + 9700q^{17} + 4014q^{19} - 39376q^{23} + 110742q^{25} - 19976q^{35} - 266500q^{39} - 106788q^{43} - 91360q^{45} + 222756q^{47} + 593586q^{49} + 540936q^{55} - 545972q^{57} - 242640q^{61} - 377716q^{63} + 545964q^{73} - 272356q^{77} + 2189926q^{81} + 1542652q^{83} - 826908q^{85} - 2729572q^{87} - 2139912q^{93} + 2142716q^{95} - 293012q^{99} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(152, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
152.7.e.a \(30\) \(34.968\) None \(0\) \(0\) \(0\) \(-720\)

Decomposition of \(S_{7}^{\mathrm{old}}(152, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(152, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 2}\)