Properties

Label 42.9.c
Level $42$
Weight $9$
Character orbit 42.c
Rep. character $\chi_{42}(13,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $1$
Sturm bound $72$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 42 = 2 \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 42.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(72\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(42, [\chi])\).

Total New Old
Modular forms 68 12 56
Cusp forms 60 12 48
Eisenstein series 8 0 8

Trace form

\( 12 q + 1536 q^{4} + 6420 q^{7} - 26244 q^{9} + O(q^{10}) \) \( 12 q + 1536 q^{4} + 6420 q^{7} - 26244 q^{9} + 4344 q^{11} - 12288 q^{14} + 59616 q^{15} + 196608 q^{16} - 224856 q^{21} - 508416 q^{22} + 499800 q^{23} - 3001476 q^{25} + 821760 q^{28} - 1278408 q^{29} + 705024 q^{30} + 2028912 q^{35} - 3359232 q^{36} + 7068648 q^{37} - 5473008 q^{39} + 1513728 q^{42} - 11388024 q^{43} + 556032 q^{44} + 8171520 q^{46} - 12346788 q^{49} + 30019584 q^{50} + 16727472 q^{51} + 19714968 q^{53} - 1572864 q^{56} - 10386144 q^{57} - 17696256 q^{58} + 7630848 q^{60} - 14040540 q^{63} + 25165824 q^{64} - 93770592 q^{65} - 9394008 q^{67} + 11218944 q^{70} + 5393208 q^{71} + 58512384 q^{74} + 24982968 q^{77} + 32638464 q^{78} + 134560968 q^{79} + 57395628 q^{81} - 28781568 q^{84} - 102074640 q^{85} - 282934272 q^{86} - 65077248 q^{88} - 96105408 q^{91} + 63974400 q^{92} + 202339296 q^{93} - 378351840 q^{95} + 387747840 q^{98} - 9500328 q^{99} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(42, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
42.9.c.a $12$ $17.110$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(6420\) \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+2^{7}q^{4}+(2\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(42, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(42, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)