Properties

Label 14.12.a
Level 14
Weight 12
Character orbit a
Rep. character \(\chi_{14}(1,\cdot)\)
Character field \(\Q\)
Dimension 6
Newforms 4
Sturm bound 24
Trace bound 2

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Defining parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 14.a (trivial)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(24\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(14))\).

Total New Old
Modular forms 24 6 18
Cusp forms 20 6 14
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.
\(+\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(4\)
Minus space\(-\)\(2\)

Trace form

\(6q \) \(\mathstrut -\mathstrut 486q^{3} \) \(\mathstrut +\mathstrut 6144q^{4} \) \(\mathstrut +\mathstrut 3874q^{5} \) \(\mathstrut -\mathstrut 12608q^{6} \) \(\mathstrut +\mathstrut 236810q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut -\mathstrut 486q^{3} \) \(\mathstrut +\mathstrut 6144q^{4} \) \(\mathstrut +\mathstrut 3874q^{5} \) \(\mathstrut -\mathstrut 12608q^{6} \) \(\mathstrut +\mathstrut 236810q^{9} \) \(\mathstrut -\mathstrut 363456q^{10} \) \(\mathstrut +\mathstrut 1323884q^{11} \) \(\mathstrut -\mathstrut 497664q^{12} \) \(\mathstrut +\mathstrut 2203470q^{13} \) \(\mathstrut +\mathstrut 1075648q^{14} \) \(\mathstrut +\mathstrut 5705912q^{15} \) \(\mathstrut +\mathstrut 6291456q^{16} \) \(\mathstrut -\mathstrut 1696024q^{17} \) \(\mathstrut +\mathstrut 8028288q^{18} \) \(\mathstrut +\mathstrut 1371822q^{19} \) \(\mathstrut +\mathstrut 3966976q^{20} \) \(\mathstrut -\mathstrut 16907842q^{21} \) \(\mathstrut -\mathstrut 177792q^{22} \) \(\mathstrut +\mathstrut 51566600q^{23} \) \(\mathstrut -\mathstrut 12910592q^{24} \) \(\mathstrut -\mathstrut 34525650q^{25} \) \(\mathstrut -\mathstrut 98434880q^{26} \) \(\mathstrut -\mathstrut 100431252q^{27} \) \(\mathstrut -\mathstrut 97880648q^{29} \) \(\mathstrut -\mathstrut 45829888q^{30} \) \(\mathstrut +\mathstrut 204823500q^{31} \) \(\mathstrut -\mathstrut 890574080q^{33} \) \(\mathstrut -\mathstrut 63911808q^{34} \) \(\mathstrut +\mathstrut 307601714q^{35} \) \(\mathstrut +\mathstrut 242493440q^{36} \) \(\mathstrut +\mathstrut 110267784q^{37} \) \(\mathstrut +\mathstrut 415977024q^{38} \) \(\mathstrut +\mathstrut 2580022976q^{39} \) \(\mathstrut -\mathstrut 372178944q^{40} \) \(\mathstrut -\mathstrut 1161081216q^{41} \) \(\mathstrut +\mathstrut 261382464q^{42} \) \(\mathstrut -\mathstrut 712891884q^{43} \) \(\mathstrut +\mathstrut 1355657216q^{44} \) \(\mathstrut +\mathstrut 3398855098q^{45} \) \(\mathstrut +\mathstrut 722366208q^{46} \) \(\mathstrut -\mathstrut 6223597068q^{47} \) \(\mathstrut -\mathstrut 509607936q^{48} \) \(\mathstrut +\mathstrut 1694851494q^{49} \) \(\mathstrut -\mathstrut 3835608704q^{50} \) \(\mathstrut +\mathstrut 6795792268q^{51} \) \(\mathstrut +\mathstrut 2256353280q^{52} \) \(\mathstrut +\mathstrut 7496822532q^{53} \) \(\mathstrut -\mathstrut 11261453696q^{54} \) \(\mathstrut -\mathstrut 7139455944q^{55} \) \(\mathstrut +\mathstrut 1101463552q^{56} \) \(\mathstrut -\mathstrut 17118924588q^{57} \) \(\mathstrut +\mathstrut 9231563136q^{58} \) \(\mathstrut -\mathstrut 20944130q^{59} \) \(\mathstrut +\mathstrut 5842853888q^{60} \) \(\mathstrut -\mathstrut 31239227502q^{61} \) \(\mathstrut +\mathstrut 731196544q^{62} \) \(\mathstrut +\mathstrut 9215547012q^{63} \) \(\mathstrut +\mathstrut 6442450944q^{64} \) \(\mathstrut +\mathstrut 14130637836q^{65} \) \(\mathstrut -\mathstrut 12745084928q^{66} \) \(\mathstrut +\mathstrut 17160124848q^{67} \) \(\mathstrut -\mathstrut 1736728576q^{68} \) \(\mathstrut +\mathstrut 15450049648q^{69} \) \(\mathstrut +\mathstrut 2223364416q^{70} \) \(\mathstrut -\mathstrut 13278746440q^{71} \) \(\mathstrut +\mathstrut 8220966912q^{72} \) \(\mathstrut +\mathstrut 51888151572q^{73} \) \(\mathstrut -\mathstrut 14296955520q^{74} \) \(\mathstrut +\mathstrut 28242983150q^{75} \) \(\mathstrut +\mathstrut 1404745728q^{76} \) \(\mathstrut +\mathstrut 6150622492q^{77} \) \(\mathstrut -\mathstrut 13353795584q^{78} \) \(\mathstrut -\mathstrut 42429894648q^{79} \) \(\mathstrut +\mathstrut 4062183424q^{80} \) \(\mathstrut +\mathstrut 8086601882q^{81} \) \(\mathstrut +\mathstrut 35503508352q^{82} \) \(\mathstrut -\mathstrut 47165805994q^{83} \) \(\mathstrut -\mathstrut 17313630208q^{84} \) \(\mathstrut +\mathstrut 22723837572q^{85} \) \(\mathstrut +\mathstrut 27251479680q^{86} \) \(\mathstrut -\mathstrut 82159329436q^{87} \) \(\mathstrut -\mathstrut 182059008q^{88} \) \(\mathstrut +\mathstrut 116340860076q^{89} \) \(\mathstrut -\mathstrut 25887488192q^{90} \) \(\mathstrut -\mathstrut 65994332586q^{91} \) \(\mathstrut +\mathstrut 52804198400q^{92} \) \(\mathstrut -\mathstrut 254334974536q^{93} \) \(\mathstrut -\mathstrut 50402446464q^{94} \) \(\mathstrut -\mathstrut 239833928104q^{95} \) \(\mathstrut -\mathstrut 13220446208q^{96} \) \(\mathstrut +\mathstrut 217462992744q^{97} \) \(\mathstrut +\mathstrut 281841334172q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(14))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7
14.12.a.a \(1\) \(10.757\) \(\Q\) None \(-32\) \(-396\) \(7350\) \(16807\) \(+\) \(-\) \(q-2^{5}q^{2}-396q^{3}+2^{10}q^{4}+7350q^{5}+\cdots\)
14.12.a.b \(1\) \(10.757\) \(\Q\) None \(32\) \(-90\) \(-7480\) \(-16807\) \(-\) \(+\) \(q+2^{5}q^{2}-90q^{3}+2^{10}q^{4}-7480q^{5}+\cdots\)
14.12.a.c \(2\) \(10.757\) \(\Q(\sqrt{153169}) \) None \(-64\) \(350\) \(266\) \(-33614\) \(+\) \(+\) \(q-2^{5}q^{2}+(175-\beta )q^{3}+2^{10}q^{4}+(133+\cdots)q^{5}+\cdots\)
14.12.a.d \(2\) \(10.757\) \(\Q(\sqrt{352969}) \) None \(64\) \(-350\) \(3738\) \(33614\) \(-\) \(-\) \(q+2^{5}q^{2}+(-175-\beta )q^{3}+2^{10}q^{4}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(14))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(14)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)