Properties

Label 81.7.b
Level $81$
Weight $7$
Character orbit 81.b
Rep. character $\chi_{81}(80,\cdot)$
Character field $\Q$
Dimension $22$
Newform subspaces $2$
Sturm bound $63$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 81 = 3^{4} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 81.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(63\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(81, [\chi])\).

Total New Old
Modular forms 60 26 34
Cusp forms 48 22 26
Eisenstein series 12 4 8

Trace form

\( 22 q - 638 q^{4} - 238 q^{7} + O(q^{10}) \) \( 22 q - 638 q^{4} - 238 q^{7} - 2004 q^{10} - 3334 q^{13} + 24718 q^{16} + 12896 q^{19} + 438 q^{22} - 33812 q^{25} - 22960 q^{28} - 24718 q^{31} - 102762 q^{34} - 77392 q^{37} + 242412 q^{40} + 76334 q^{43} + 325668 q^{46} - 283752 q^{49} + 215216 q^{52} + 32610 q^{55} - 217344 q^{58} - 507730 q^{61} - 1599998 q^{64} + 736574 q^{67} + 1296924 q^{70} + 2090600 q^{73} - 2345038 q^{76} - 2614 q^{79} + 52806 q^{82} + 2111724 q^{85} - 1896162 q^{88} - 817682 q^{91} + 4629480 q^{94} - 1023322 q^{97} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(81, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
81.7.b.a 81.b 3.b $10$ $18.634$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 9.7.d.a \(0\) \(0\) \(0\) \(242\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(-5^{2}-\beta _{2})q^{4}+\beta _{6}q^{5}+\cdots\)
81.7.b.b 81.b 3.b $12$ $18.634$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 81.7.b.b \(0\) \(0\) \(0\) \(-480\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(-2^{5}+\beta _{1})q^{4}+(-2\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(81, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(81, [\chi]) \simeq \) \(S_{7}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)