Properties

Label 207.6.a
Level $207$
Weight $6$
Character orbit 207.a
Rep. character $\chi_{207}(1,\cdot)$
Character field $\Q$
Dimension $47$
Newform subspaces $9$
Sturm bound $144$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 207 = 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 207.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(144\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(207))\).

Total New Old
Modular forms 124 47 77
Cusp forms 116 47 69
Eisenstein series 8 0 8

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)\(23\)FrickeDim.
\(+\)\(+\)\(+\)\(10\)
\(+\)\(-\)\(-\)\(10\)
\(-\)\(+\)\(-\)\(15\)
\(-\)\(-\)\(+\)\(12\)
Plus space\(+\)\(22\)
Minus space\(-\)\(25\)

Trace form

\( 47 q - 8 q^{2} + 800 q^{4} - 16 q^{5} + 98 q^{7} + 75 q^{8} + O(q^{10}) \) \( 47 q - 8 q^{2} + 800 q^{4} - 16 q^{5} + 98 q^{7} + 75 q^{8} - 294 q^{10} - 78 q^{11} - 552 q^{13} + 1052 q^{14} + 16128 q^{16} + 2784 q^{17} - 2728 q^{19} - 3968 q^{20} - 7940 q^{22} - 1587 q^{23} + 23501 q^{25} - 8877 q^{26} + 14610 q^{28} - 2532 q^{29} - 2712 q^{31} + 6732 q^{32} + 3322 q^{34} + 8800 q^{35} + 10544 q^{37} + 46792 q^{38} - 1834 q^{40} - 13328 q^{41} - 11700 q^{43} - 7598 q^{44} + 4232 q^{46} - 65184 q^{47} + 151075 q^{49} + 87608 q^{50} - 68469 q^{52} + 104810 q^{53} + 19556 q^{55} + 56746 q^{56} - 105237 q^{58} - 5848 q^{59} - 56354 q^{61} - 38037 q^{62} + 284467 q^{64} + 95190 q^{65} - 29182 q^{67} + 2728 q^{68} + 112220 q^{70} - 94964 q^{71} + 105892 q^{73} + 34770 q^{74} - 257848 q^{76} - 36656 q^{77} - 10540 q^{79} - 159690 q^{80} - 143843 q^{82} + 62362 q^{83} + 175676 q^{85} - 7806 q^{86} - 106460 q^{88} - 354426 q^{89} - 428658 q^{91} - 50784 q^{92} + 185761 q^{94} - 47476 q^{95} - 181052 q^{97} + 325756 q^{98} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(207))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 23
207.6.a.a $2$ $33.199$ \(\Q(\sqrt{29}) \) None \(0\) \(0\) \(-94\) \(-118\) $-$ $+$ \(q-2\beta q^{2}+84q^{4}+(-47-\beta )q^{5}+(-59+\cdots)q^{7}+\cdots\)
207.6.a.b $3$ $33.199$ 3.3.7925.1 None \(4\) \(0\) \(58\) \(-282\) $-$ $-$ \(q+(1-\beta _{1})q^{2}+(2-6\beta _{1}+4\beta _{2})q^{4}+\cdots\)
207.6.a.c $3$ $33.199$ 3.3.5333.1 None \(8\) \(0\) \(56\) \(-114\) $-$ $+$ \(q+(3-\beta _{2})q^{2}+(9-4\beta _{1}-9\beta _{2})q^{4}+\cdots\)
207.6.a.d $4$ $33.199$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-4\) \(0\) \(122\) \(62\) $-$ $+$ \(q+(-1-\beta _{1})q^{2}+(-12+4\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
207.6.a.e $4$ $33.199$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-4\) \(0\) \(-22\) \(-62\) $-$ $-$ \(q+(-1+\beta _{1})q^{2}+(7-\beta _{1}+\beta _{3})q^{4}+\cdots\)
207.6.a.f $5$ $33.199$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-8\) \(0\) \(-94\) \(272\) $-$ $-$ \(q+(-2+\beta _{2})q^{2}+(24-\beta _{2}+\beta _{3})q^{4}+\cdots\)
207.6.a.g $6$ $33.199$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-4\) \(0\) \(-42\) \(300\) $-$ $+$ \(q+(-1+\beta _{1})q^{2}+(20-2\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
207.6.a.h $10$ $33.199$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-8\) \(0\) \(-100\) \(20\) $+$ $+$ \(q+(-1+\beta _{1})q^{2}+(19-\beta _{1}+\beta _{2})q^{4}+\cdots\)
207.6.a.i $10$ $33.199$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(8\) \(0\) \(100\) \(20\) $+$ $-$ \(q+(1-\beta _{1})q^{2}+(19-\beta _{1}+\beta _{2})q^{4}+(9+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(207))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(207)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 2}\)