Properties

Label 76.3.c
Level $76$
Weight $3$
Character orbit 76.c
Rep. character $\chi_{76}(37,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $30$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
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: \(30\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(76, [\chi])\).

Total New Old
Modular forms 23 4 19
Cusp forms 17 4 13
Eisenstein series 6 0 6

Trace form

\( 4q + q^{5} + 3q^{7} - 22q^{9} + O(q^{10}) \) \( 4q + q^{5} + 3q^{7} - 22q^{9} + 25q^{11} + 31q^{17} - 18q^{19} - 62q^{23} + q^{25} - 55q^{35} - 174q^{39} + 221q^{43} + 241q^{45} - 23q^{47} + 75q^{49} + 17q^{55} - 174q^{57} - 183q^{61} + 85q^{63} + 11q^{73} - 463q^{77} + 440q^{81} + 244q^{83} - 451q^{85} + 522q^{87} + 348q^{93} - 251q^{95} - 587q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(76, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
76.3.c.a \(2\) \(2.071\) \(\Q(\sqrt{-29}) \) None \(0\) \(0\) \(-8\) \(-2\) \(q+\beta q^{3}-4q^{5}-q^{7}-20q^{9}+14q^{11}+\cdots\)
76.3.c.b \(2\) \(2.071\) \(\Q(\sqrt{57}) \) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(9\) \(5\) \(q+(5-\beta )q^{5}+(1+3\beta )q^{7}+9q^{9}+(1+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(76, [\chi])\) into lower level spaces

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