Properties

Label 304.2.h
Level $304$
Weight $2$
Character orbit 304.h
Rep. character $\chi_{304}(303,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $3$
Sturm bound $80$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 304.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(80\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(304, [\chi])\).

Total New Old
Modular forms 46 10 36
Cusp forms 34 10 24
Eisenstein series 12 0 12

Trace form

\( 10 q - 2 q^{9} + O(q^{10}) \) \( 10 q - 2 q^{9} + 12 q^{17} + 10 q^{25} - 26 q^{49} - 28 q^{57} - 32 q^{61} - 44 q^{73} + 12 q^{77} + 34 q^{81} + 36 q^{85} - 56 q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(304, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
304.2.h.a 304.h 76.d $2$ $2.427$ \(\Q(\sqrt{-19}) \) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(-2\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-q^{5}-\beta q^{7}-3q^{9}-\beta q^{11}+7q^{17}+\cdots\)
304.2.h.b 304.h 76.d $4$ $2.427$ \(\Q(\sqrt{-3}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-\beta _{2}q^{7}+4q^{9}+2\beta _{2}q^{11}+\cdots\)
304.2.h.c 304.h 76.d $4$ $2.427$ \(\Q(\sqrt{-3}, \sqrt{-19})\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(2\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(1-\beta _{2})q^{5}+(2\beta _{1}+\beta _{3})q^{7}-3q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(304, [\chi])\) into lower level spaces

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