Properties

Label 304.7.e
Level $304$
Weight $7$
Character orbit 304.e
Rep. character $\chi_{304}(113,\cdot)$
Character field $\Q$
Dimension $59$
Newform subspaces $6$
Sturm bound $280$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 304.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(280\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(304, [\chi])\).

Total New Old
Modular forms 246 61 185
Cusp forms 234 59 175
Eisenstein series 12 2 10

Trace form

\( 59q - 2q^{5} + 722q^{7} - 14773q^{9} + O(q^{10}) \) \( 59q - 2q^{5} + 722q^{7} - 14773q^{9} + 2q^{11} + 6838q^{17} + 7009q^{19} + 8906q^{23} + 171873q^{25} + 7156q^{35} + 134624q^{39} + 174722q^{43} - 29794q^{45} + 125666q^{47} + 857073q^{49} - 392036q^{55} - 367288q^{57} - 502898q^{61} + 704866q^{63} - 613082q^{73} + 5740q^{77} + 2946235q^{81} + 1027698q^{83} - 309844q^{85} + 904272q^{87} - 1328240q^{93} - 3493070q^{95} - 431246q^{99} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(304, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
304.7.e.a \(1\) \(69.936\) \(\Q\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(-54\) \(-610\) \(q-54q^{5}-610q^{7}+3^{6}q^{9}+1062q^{11}+\cdots\)
304.7.e.b \(2\) \(69.936\) \(\Q(\sqrt{57}) \) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(54\) \(610\) \(q+(3^{3}+7\beta )q^{5}+(305-9\beta )q^{7}+3^{6}q^{9}+\cdots\)
304.7.e.c \(8\) \(69.936\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(2\) \(-362\) \(q+\beta _{1}q^{3}+\beta _{7}q^{5}+(-46-\beta _{2}-2\beta _{3}+\cdots)q^{7}+\cdots\)
304.7.e.d \(8\) \(69.936\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(108\) \(140\) \(q+\beta _{1}q^{3}+(13-\beta _{5})q^{5}+(18-2\beta _{3}+\cdots)q^{7}+\cdots\)
304.7.e.e \(10\) \(69.936\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(-112\) \(224\) \(q-\beta _{5}q^{3}+(-11-\beta _{1})q^{5}+(23-2\beta _{1}+\cdots)q^{7}+\cdots\)
304.7.e.f \(30\) \(69.936\) None \(0\) \(0\) \(0\) \(720\)

Decomposition of \(S_{7}^{\mathrm{old}}(304, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(304, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 2}\)