Properties

Label 76.7.c
Level $76$
Weight $7$
Character orbit 76.c
Rep. character $\chi_{76}(37,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $2$
Sturm bound $70$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 76.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(70\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(76, [\chi])\).

Total New Old
Modular forms 63 10 53
Cusp forms 57 10 47
Eisenstein series 6 0 6

Trace form

\( 10q + 56q^{5} - 248q^{7} - 2890q^{9} + O(q^{10}) \) \( 10q + 56q^{5} - 248q^{7} - 2890q^{9} + 1964q^{11} + 11180q^{17} - 7486q^{19} + 22400q^{23} + 47426q^{25} - 3320q^{35} + 167028q^{39} - 192412q^{43} - 17864q^{45} - 495244q^{47} + 546678q^{49} + 224112q^{55} + 341316q^{57} - 574952q^{61} - 116516q^{63} - 1236988q^{73} + 377500q^{77} - 756574q^{81} - 1820860q^{83} - 853356q^{85} + 1483380q^{87} + 2131176q^{93} + 257564q^{95} - 91196q^{99} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(76, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
76.7.c.a \(2\) \(17.484\) \(\Q(\sqrt{57}) \) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(54\) \(-610\) \(q+(3^{3}+7\beta )q^{5}+(-305+9\beta )q^{7}+3^{6}q^{9}+\cdots\)
76.7.c.b \(8\) \(17.484\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(2\) \(362\) \(q+\beta _{1}q^{3}+\beta _{7}q^{5}+(46+\beta _{2}+2\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(76, [\chi])\) into lower level spaces

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