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Properties

Label 27.7.b
Level $27$
Weight $7$
Character orbit 27.b
Rep. character $\chi_{27}(26,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $3$
Sturm bound $21$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 27 = 3^{3} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 27.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(21\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(27, [\chi])\).

Total New Old
Modular forms 21 8 13
Cusp forms 15 8 7
Eisenstein series 6 0 6

Trace form

\( 8 q - 190 q^{4} - 884 q^{7} + O(q^{10}) \) \( 8 q - 190 q^{4} - 884 q^{7} + 3618 q^{10} - 380 q^{13} - 2710 q^{16} + 7360 q^{19} - 22086 q^{22} - 70588 q^{25} + 190042 q^{28} - 44876 q^{31} - 138996 q^{34} + 242476 q^{37} - 168858 q^{40} - 136856 q^{43} - 145584 q^{46} + 154896 q^{49} + 117808 q^{52} + 152820 q^{55} + 329292 q^{58} + 590092 q^{61} - 711442 q^{64} - 1031672 q^{67} - 228150 q^{70} - 1683920 q^{73} + 3206788 q^{76} + 2362264 q^{79} - 3502872 q^{82} - 1833192 q^{85} + 1796958 q^{88} + 1892840 q^{91} + 1845612 q^{94} - 977960 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(27, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
27.7.b.a 27.b 3.b $2$ $6.211$ \(\Q(\sqrt{-10}) \) None 27.7.b.a \(0\) \(0\) \(0\) \(-806\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}-26q^{4}+14\beta q^{5}-403q^{7}+\cdots\)
27.7.b.b 27.b 3.b $2$ $6.211$ \(\Q(\sqrt{-1}) \) None 27.7.b.b \(0\) \(0\) \(0\) \(598\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}+28 q^{4}-40\beta q^{5}+299 q^{7}+\cdots\)
27.7.b.c 27.b 3.b $4$ $6.211$ \(\Q(i, \sqrt{41})\) None 27.7.b.c \(0\) \(0\) \(0\) \(-676\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(-7^{2}+\beta _{3})q^{4}+(7\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(27, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(27, [\chi]) \simeq \) \(S_{7}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)