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Properties

Label 126.14.a
Level $126$
Weight $14$
Character orbit 126.a
Rep. character $\chi_{126}(1,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $17$
Sturm bound $336$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 126.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 17 \)
Sturm bound: \(336\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(126))\).

Total New Old
Modular forms 320 32 288
Cusp forms 304 32 272
Eisenstein series 16 0 16

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

\(2\)\(3\)\(7\)FrickeDim
\(+\)\(+\)\(+\)$+$\(3\)
\(+\)\(+\)\(-\)$-$\(3\)
\(+\)\(-\)\(+\)$-$\(5\)
\(+\)\(-\)\(-\)$+$\(4\)
\(-\)\(+\)\(+\)$-$\(3\)
\(-\)\(+\)\(-\)$+$\(3\)
\(-\)\(-\)\(+\)$+$\(5\)
\(-\)\(-\)\(-\)$-$\(6\)
Plus space\(+\)\(15\)
Minus space\(-\)\(17\)

Trace form

\( 32 q + 128 q^{2} + 131072 q^{4} - 91578 q^{5} + 524288 q^{8} + O(q^{10}) \) \( 32 q + 128 q^{2} + 131072 q^{4} - 91578 q^{5} + 524288 q^{8} + 3261568 q^{10} + 9735852 q^{11} - 35071450 q^{13} + 15059072 q^{14} + 536870912 q^{16} + 72529284 q^{17} + 276742198 q^{19} - 375103488 q^{20} - 1301617408 q^{22} - 2033890824 q^{23} + 5501934924 q^{25} - 211760000 q^{26} + 2472927516 q^{29} - 21435764788 q^{31} + 2147483648 q^{32} + 942182912 q^{34} + 7022939406 q^{35} - 7370960372 q^{37} + 64376618368 q^{38} + 13359382528 q^{40} - 70809061428 q^{41} + 135632662684 q^{43} + 39878049792 q^{44} - 150988412416 q^{46} - 343835338980 q^{47} + 442921190432 q^{49} + 291097637504 q^{50} - 143652659200 q^{52} - 176197912296 q^{53} + 99718346120 q^{55} + 61681958912 q^{56} - 125490027008 q^{58} - 77658461574 q^{59} - 967000636462 q^{61} + 335189801728 q^{62} + 2199023255552 q^{64} - 2143321196892 q^{65} + 1200939985128 q^{67} + 297079947264 q^{68} + 580632639104 q^{70} - 948080855304 q^{71} + 2123793354552 q^{73} + 4906978816 q^{74} + 1133536043008 q^{76} - 224557587492 q^{77} - 3942873248584 q^{79} - 1536423886848 q^{80} - 1921048522752 q^{82} + 8067875511042 q^{83} + 155496902132 q^{85} - 8789756052224 q^{86} - 5331424903168 q^{88} + 5094054891240 q^{89} - 3324716739274 q^{91} - 8330816815104 q^{92} + 21378019252992 q^{94} - 7400544829080 q^{95} - 42314619560220 q^{97} + 1771684761728 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(126))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 7
126.14.a.a 126.a 1.a $1$ $135.111$ \(\Q\) None \(-64\) \(0\) \(-4320\) \(117649\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2^{6}q^{2}+2^{12}q^{4}-4320q^{5}+7^{6}q^{7}+\cdots\)
126.14.a.b 126.a 1.a $1$ $135.111$ \(\Q\) None \(-64\) \(0\) \(22370\) \(-117649\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2^{6}q^{2}+2^{12}q^{4}+22370q^{5}-7^{6}q^{7}+\cdots\)
126.14.a.c 126.a 1.a $1$ $135.111$ \(\Q\) None \(-64\) \(0\) \(30330\) \(117649\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2^{6}q^{2}+2^{12}q^{4}+30330q^{5}+7^{6}q^{7}+\cdots\)
126.14.a.d 126.a 1.a $1$ $135.111$ \(\Q\) None \(64\) \(0\) \(-34758\) \(117649\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2^{6}q^{2}+2^{12}q^{4}-34758q^{5}+7^{6}q^{7}+\cdots\)
126.14.a.e 126.a 1.a $1$ $135.111$ \(\Q\) None \(64\) \(0\) \(36400\) \(-117649\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2^{6}q^{2}+2^{12}q^{4}+36400q^{5}-7^{6}q^{7}+\cdots\)
126.14.a.f 126.a 1.a $1$ $135.111$ \(\Q\) None \(64\) \(0\) \(51720\) \(117649\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2^{6}q^{2}+2^{12}q^{4}+51720q^{5}+7^{6}q^{7}+\cdots\)
126.14.a.g 126.a 1.a $2$ $135.111$ \(\Q(\sqrt{78985}) \) None \(-128\) \(0\) \(-75530\) \(-235298\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2^{6}q^{2}+2^{12}q^{4}+(-37765-13\beta )q^{5}+\cdots\)
126.14.a.h 126.a 1.a $2$ $135.111$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(-128\) \(0\) \(-37374\) \(235298\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2^{6}q^{2}+2^{12}q^{4}+(-18687-\beta )q^{5}+\cdots\)
126.14.a.i 126.a 1.a $2$ $135.111$ \(\Q(\sqrt{305281}) \) None \(-128\) \(0\) \(27574\) \(-235298\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2^{6}q^{2}+2^{12}q^{4}+(13787-19\beta )q^{5}+\cdots\)
126.14.a.j 126.a 1.a $2$ $135.111$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(128\) \(0\) \(-46474\) \(-235298\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2^{6}q^{2}+2^{12}q^{4}+(-23237-\beta )q^{5}+\cdots\)
126.14.a.k 126.a 1.a $2$ $135.111$ \(\Q(\sqrt{407521}) \) None \(128\) \(0\) \(-39976\) \(-235298\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2^{6}q^{2}+2^{12}q^{4}+(-19988-\beta )q^{5}+\cdots\)
126.14.a.l 126.a 1.a $2$ $135.111$ \(\Q(\sqrt{100129}) \) None \(128\) \(0\) \(-32004\) \(235298\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2^{6}q^{2}+2^{12}q^{4}+(-16002-7\beta )q^{5}+\cdots\)
126.14.a.m 126.a 1.a $2$ $135.111$ \(\Q(\sqrt{601441}) \) None \(128\) \(0\) \(10464\) \(235298\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2^{6}q^{2}+2^{12}q^{4}+(5232-\beta )q^{5}+\cdots\)
126.14.a.n 126.a 1.a $3$ $135.111$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-192\) \(0\) \(-28626\) \(352947\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2^{6}q^{2}+2^{12}q^{4}+(-9542-\beta _{1}+\cdots)q^{5}+\cdots\)
126.14.a.o 126.a 1.a $3$ $135.111$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-192\) \(0\) \(-5694\) \(-352947\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2^{6}q^{2}+2^{12}q^{4}+(-1898+\beta _{1}+\cdots)q^{5}+\cdots\)
126.14.a.p 126.a 1.a $3$ $135.111$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(192\) \(0\) \(5694\) \(-352947\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2^{6}q^{2}+2^{12}q^{4}+(1898-\beta _{1})q^{5}+\cdots\)
126.14.a.q 126.a 1.a $3$ $135.111$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(192\) \(0\) \(28626\) \(352947\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2^{6}q^{2}+2^{12}q^{4}+(9542+\beta _{1})q^{5}+\cdots\)

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_0(126))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_0(126)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 2}\)