Properties

Label 36.7.c
Level $36$
Weight $7$
Character orbit 36.c
Rep. character $\chi_{36}(17,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $42$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 36.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(42\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(36, [\chi])\).

Total New Old
Modular forms 42 2 40
Cusp forms 30 2 28
Eisenstein series 12 0 12

Trace form

\( 2 q - 488 q^{7} + O(q^{10}) \) \( 2 q - 488 q^{7} - 5456 q^{13} - 10784 q^{19} + 23150 q^{25} + 20344 q^{31} + 130012 q^{37} - 98960 q^{43} - 116226 q^{49} - 304560 q^{55} + 201220 q^{61} - 871472 q^{67} + 1239136 q^{73} + 1028680 q^{79} - 750060 q^{85} + 1331264 q^{91} + 85408 q^{97} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(36, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
36.7.c.a 36.c 3.b $2$ $8.282$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-488\) $\mathrm{SU}(2)[C_{2}]$ \(q+5\beta q^{5}-244q^{7}+188\beta q^{11}-2728q^{13}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(36, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(36, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)