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Properties

Label 3.14.a
Level $3$
Weight $14$
Character orbit 3.a
Rep. character $\chi_{3}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $2$
Sturm bound $4$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 3.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(4\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(3))\).

Total New Old
Modular forms 5 3 2
Cusp forms 3 3 0
Eisenstein series 2 0 2

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

\(3\)Dim
\(+\)\(1\)
\(-\)\(2\)

Trace form

\( 3 q - 66 q^{2} + 729 q^{3} + 12468 q^{4} + 10506 q^{5} - 30618 q^{6} + 214080 q^{7} - 1830552 q^{8} + 1594323 q^{9} + O(q^{10}) \) \( 3 q - 66 q^{2} + 729 q^{3} + 12468 q^{4} + 10506 q^{5} - 30618 q^{6} + 214080 q^{7} - 1830552 q^{8} + 1594323 q^{9} + 3799764 q^{10} - 10510500 q^{11} + 20823156 q^{12} + 25582218 q^{13} - 124741392 q^{14} + 51705054 q^{15} + 75107856 q^{16} - 33656058 q^{17} - 35075106 q^{18} + 42232164 q^{19} + 415819704 q^{20} - 186693984 q^{21} - 1181420856 q^{22} + 1690137480 q^{23} - 1618607448 q^{24} - 1339887219 q^{25} + 2614700676 q^{26} + 387420489 q^{27} + 4506839520 q^{28} - 5980875582 q^{29} + 2241473796 q^{30} + 176798904 q^{31} - 9664679520 q^{32} + 8642525364 q^{33} + 1732142556 q^{34} - 23208096000 q^{35} + 6626006388 q^{36} + 21913002690 q^{37} + 22841047416 q^{38} + 6913099710 q^{39} - 31134175632 q^{40} + 10580286414 q^{41} - 86823375120 q^{42} - 4199485476 q^{43} + 166960484592 q^{44} + 5583319146 q^{45} - 164218913136 q^{46} - 98563919232 q^{47} - 37961549424 q^{48} + 188136984267 q^{49} + 216267297954 q^{50} + 146771892594 q^{51} - 56906364648 q^{52} - 430461936630 q^{53} - 16271660538 q^{54} + 185449558536 q^{55} - 364557046080 q^{56} + 342888739596 q^{57} + 359196653412 q^{58} - 957730645284 q^{59} - 51351092424 q^{60} + 45003454602 q^{61} + 1329517977600 q^{62} + 113770889280 q^{63} - 571959536064 q^{64} + 521388486348 q^{65} - 1056911962392 q^{66} - 349796259228 q^{67} + 1665976898088 q^{68} + 21160239768 q^{69} - 2021165313120 q^{70} + 529876859256 q^{71} - 972830385432 q^{72} + 678524322750 q^{73} - 1288521504492 q^{74} - 527627724201 q^{75} + 2883444387216 q^{76} + 1847993854080 q^{77} + 2046952839348 q^{78} - 1786446129720 q^{79} - 4705679741856 q^{80} + 847288609443 q^{81} + 3119523017580 q^{82} - 3450268778268 q^{83} + 6044004840672 q^{84} + 5587286601492 q^{85} - 10824101299320 q^{86} - 2534058734778 q^{87} - 7432535084832 q^{88} + 5505789611214 q^{89} + 2019350379924 q^{90} - 9298036288896 q^{91} + 9209631335520 q^{92} - 8851446703800 q^{93} + 26697141090720 q^{94} + 15165024536184 q^{95} - 3605335005024 q^{96} - 24090183321978 q^{97} - 3130819722738 q^{98} - 5585710630500 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(3))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3
3.14.a.a 3.a 1.a $1$ $3.217$ \(\Q\) None \(-12\) \(-729\) \(-30210\) \(235088\) $+$ $\mathrm{SU}(2)$ \(q-12q^{2}-3^{6}q^{3}-8048q^{4}-30210q^{5}+\cdots\)
3.14.a.b 3.a 1.a $2$ $3.217$ \(\Q(\sqrt{1969}) \) None \(-54\) \(1458\) \(40716\) \(-21008\) $-$ $\mathrm{SU}(2)$ \(q+(-3^{3}-\beta )q^{2}+3^{6}q^{3}+(10258+54\beta )q^{4}+\cdots\)