Properties

Label 304.1.e
Level $304$
Weight $1$
Character orbit 304.e
Rep. character $\chi_{304}(113,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $40$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 304.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(40\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(304, [\chi])\).

Total New Old
Modular forms 10 2 8
Cusp forms 4 1 3
Eisenstein series 6 1 5

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 1 0 0 0

Trace form

\( q - q^{5} + q^{7} + q^{9} + O(q^{10}) \) \( q - q^{5} + q^{7} + q^{9} + q^{11} - q^{17} - q^{19} - 2 q^{23} - q^{35} + q^{43} - q^{45} + q^{47} - q^{55} - q^{61} + q^{63} - q^{73} + q^{77} + q^{81} - 2 q^{83} + q^{85} + q^{95} + q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(304, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
304.1.e.a 304.e 19.b $1$ $0.152$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-19}) \) None 76.1.c.a \(0\) \(0\) \(-1\) \(1\) \(q-q^{5}+q^{7}+q^{9}+q^{11}-q^{17}-q^{19}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(304, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(304, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 2}\)