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Properties

Label 14.16.a
Level $14$
Weight $16$
Character orbit 14.a
Rep. character $\chi_{14}(1,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $4$
Sturm bound $32$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 16 \)
Character orbit: \([\chi]\) \(=\) 14.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(32\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_0(14))\).

Total New Old
Modular forms 32 8 24
Cusp forms 28 8 20
Eisenstein series 4 0 4

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

\(2\)\(7\)FrickeDim
\(+\)\(+\)$+$\(2\)
\(+\)\(-\)$-$\(1\)
\(-\)\(+\)$-$\(2\)
\(-\)\(-\)$+$\(3\)
Plus space\(+\)\(5\)
Minus space\(-\)\(3\)

Trace form

\( 8 q + 256 q^{2} - 8130 q^{3} + 131072 q^{4} - 25926 q^{5} - 185600 q^{6} + 4194304 q^{8} + 15306476 q^{9} + O(q^{10}) \) \( 8 q + 256 q^{2} - 8130 q^{3} + 131072 q^{4} - 25926 q^{5} - 185600 q^{6} + 4194304 q^{8} + 15306476 q^{9} + 37406464 q^{10} + 22651932 q^{11} - 133201920 q^{12} - 351841858 q^{13} + 210827008 q^{14} - 280251208 q^{15} + 2147483648 q^{16} - 732728268 q^{17} + 9610596096 q^{18} - 11628612038 q^{19} - 424771584 q^{20} + 13550576522 q^{21} + 10492416512 q^{22} + 19052477880 q^{23} - 3040870400 q^{24} + 133541322180 q^{25} - 13699450624 q^{26} + 17152537716 q^{27} + 37244220684 q^{29} - 114663083008 q^{30} + 49216127012 q^{31} + 68719476736 q^{32} + 1223151148816 q^{33} - 194994549760 q^{34} - 189729483426 q^{35} + 250781302784 q^{36} - 623389364948 q^{37} + 90195355904 q^{38} - 1283475734704 q^{39} + 612867506176 q^{40} - 4617723051684 q^{41} + 461078666496 q^{42} - 2718570441644 q^{43} + 371129253888 q^{44} + 4972004158978 q^{45} + 1199523550208 q^{46} - 14176898095620 q^{47} - 2182380257280 q^{48} + 5425784582792 q^{49} - 3487705819904 q^{50} + 6318498765604 q^{51} - 5764577001472 q^{52} + 10311567439296 q^{53} - 15761003781632 q^{54} + 5241115548296 q^{55} + 3454189699072 q^{56} + 30418034645148 q^{57} + 8384613809152 q^{58} - 11249706779526 q^{59} - 4591635791872 q^{60} - 16868999086054 q^{61} + 14764167918080 q^{62} + 140242784556 q^{63} + 35184372088832 q^{64} + 112667788253916 q^{65} + 59116108257280 q^{66} + 83707932210024 q^{67} - 12005019942912 q^{68} - 60881399817152 q^{69} - 23644881428224 q^{70} - 291504937736184 q^{71} + 157460006436864 q^{72} + 267628193084328 q^{73} + 200996330046464 q^{74} - 859650232817590 q^{75} - 190523179630592 q^{76} + 203037091703796 q^{77} - 417829807529984 q^{78} + 204144141980360 q^{79} - 6959457632256 q^{80} + 1258211420958932 q^{81} - 962336312174592 q^{82} - 456972975850110 q^{83} + 222012645736448 q^{84} - 841608962840428 q^{85} + 200789926776320 q^{86} + 720803618326220 q^{87} + 171907752132608 q^{88} - 2110704983009808 q^{89} + 484333674988288 q^{90} + 932507600003882 q^{91} + 312155797585920 q^{92} + 461803859335880 q^{93} - 68123166159360 q^{94} + 1253520098241816 q^{95} - 49821620633600 q^{96} - 1169857172772396 q^{97} + 173625106649344 q^{98} - 1512609592308532 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_0(14))\) 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 7
14.16.a.a 14.a 1.a $1$ $19.977$ \(\Q\) None \(-128\) \(1350\) \(-81060\) \(823543\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2^{7}q^{2}+1350q^{3}+2^{14}q^{4}-81060q^{5}+\cdots\)
14.16.a.b 14.a 1.a $2$ $19.977$ \(\Q(\sqrt{169009}) \) None \(-256\) \(-4690\) \(-78022\) \(-1647086\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2^{7}q^{2}+(-2345-\beta )q^{3}+2^{14}q^{4}+\cdots\)
14.16.a.c 14.a 1.a $2$ $19.977$ \(\Q(\sqrt{54961}) \) None \(256\) \(-7602\) \(180250\) \(-1647086\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2^{7}q^{2}+(-3801-\beta )q^{3}+2^{14}q^{4}+\cdots\)
14.16.a.d 14.a 1.a $3$ $19.977$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(384\) \(2812\) \(-47094\) \(2470629\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2^{7}q^{2}+(937+\beta _{1})q^{3}+2^{14}q^{4}+\cdots\)

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_0(14))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_0(14)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)