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 $5$

Related objects

Downloads

Learn more about

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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
304.2.h.a \(2\) \(2.427\) \(\Q(\sqrt{-19}) \) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(-2\) \(0\) \(q-q^{5}-\beta q^{7}-3q^{9}-\beta q^{11}+7q^{17}+\cdots\)
304.2.h.b \(4\) \(2.427\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{2}q^{7}+4q^{9}+2\beta _{2}q^{11}+\cdots\)
304.2.h.c \(4\) \(2.427\) \(\Q(\sqrt{-3}, \sqrt{-19})\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(2\) \(0\) \(q+(1-\beta _{2})q^{5}+(2\beta _{1}+\beta _{3})q^{7}-3q^{9}+\cdots\)

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

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