Properties

Label 7.12.a
Level 7
Weight 12
Character orbit a
Rep. character \(\chi_{7}(1,\cdot)\)
Character field \(\Q\)
Dimension 5
Newforms 2
Sturm bound 8
Trace bound 1

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 7.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(8\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(7))\).

Total New Old
Modular forms 9 5 4
Cusp forms 7 5 2
Eisenstein series 2 0 2

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

\(7\)Dim.
\(+\)\(3\)
\(-\)\(2\)

Trace form

\(5q \) \(\mathstrut +\mathstrut 23q^{2} \) \(\mathstrut -\mathstrut 20q^{3} \) \(\mathstrut +\mathstrut 9593q^{4} \) \(\mathstrut -\mathstrut 8474q^{5} \) \(\mathstrut +\mathstrut 20606q^{6} \) \(\mathstrut -\mathstrut 16807q^{7} \) \(\mathstrut -\mathstrut 238857q^{8} \) \(\mathstrut +\mathstrut 553993q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(5q \) \(\mathstrut +\mathstrut 23q^{2} \) \(\mathstrut -\mathstrut 20q^{3} \) \(\mathstrut +\mathstrut 9593q^{4} \) \(\mathstrut -\mathstrut 8474q^{5} \) \(\mathstrut +\mathstrut 20606q^{6} \) \(\mathstrut -\mathstrut 16807q^{7} \) \(\mathstrut -\mathstrut 238857q^{8} \) \(\mathstrut +\mathstrut 553993q^{9} \) \(\mathstrut +\mathstrut 1042644q^{10} \) \(\mathstrut -\mathstrut 1789868q^{11} \) \(\mathstrut +\mathstrut 1819958q^{12} \) \(\mathstrut -\mathstrut 1890770q^{13} \) \(\mathstrut -\mathstrut 2201717q^{14} \) \(\mathstrut -\mathstrut 9435032q^{15} \) \(\mathstrut +\mathstrut 2149889q^{16} \) \(\mathstrut +\mathstrut 19957386q^{17} \) \(\mathstrut -\mathstrut 1990249q^{18} \) \(\mathstrut -\mathstrut 5658356q^{19} \) \(\mathstrut +\mathstrut 6668648q^{20} \) \(\mathstrut +\mathstrut 4369820q^{21} \) \(\mathstrut +\mathstrut 80192256q^{22} \) \(\mathstrut -\mathstrut 58884264q^{23} \) \(\mathstrut -\mathstrut 198158526q^{24} \) \(\mathstrut +\mathstrut 63067331q^{25} \) \(\mathstrut +\mathstrut 67980080q^{26} \) \(\mathstrut +\mathstrut 207253576q^{27} \) \(\mathstrut -\mathstrut 23412151q^{28} \) \(\mathstrut -\mathstrut 65337794q^{29} \) \(\mathstrut -\mathstrut 265674448q^{30} \) \(\mathstrut +\mathstrut 146902960q^{31} \) \(\mathstrut -\mathstrut 473095673q^{32} \) \(\mathstrut +\mathstrut 573117184q^{33} \) \(\mathstrut -\mathstrut 212873502q^{34} \) \(\mathstrut -\mathstrut 311366482q^{35} \) \(\mathstrut +\mathstrut 375771185q^{36} \) \(\mathstrut +\mathstrut 39902998q^{37} \) \(\mathstrut +\mathstrut 468983810q^{38} \) \(\mathstrut -\mathstrut 1868351576q^{39} \) \(\mathstrut +\mathstrut 4382370240q^{40} \) \(\mathstrut +\mathstrut 715406594q^{41} \) \(\mathstrut -\mathstrut 1814181194q^{42} \) \(\mathstrut +\mathstrut 2286943060q^{43} \) \(\mathstrut -\mathstrut 4718958808q^{44} \) \(\mathstrut -\mathstrut 4391788658q^{45} \) \(\mathstrut -\mathstrut 4651377792q^{46} \) \(\mathstrut +\mathstrut 3292066368q^{47} \) \(\mathstrut +\mathstrut 4287400094q^{48} \) \(\mathstrut +\mathstrut 1412376245q^{49} \) \(\mathstrut +\mathstrut 10622634109q^{50} \) \(\mathstrut -\mathstrut 6461937192q^{51} \) \(\mathstrut -\mathstrut 15294285692q^{52} \) \(\mathstrut -\mathstrut 4092389850q^{53} \) \(\mathstrut +\mathstrut 32250303908q^{54} \) \(\mathstrut +\mathstrut 1274569032q^{55} \) \(\mathstrut -\mathstrut 8219681841q^{56} \) \(\mathstrut +\mathstrut 5946205456q^{57} \) \(\mathstrut -\mathstrut 17444657898q^{58} \) \(\mathstrut +\mathstrut 9010519428q^{59} \) \(\mathstrut -\mathstrut 34060585216q^{60} \) \(\mathstrut +\mathstrut 17149402798q^{61} \) \(\mathstrut +\mathstrut 13269410460q^{62} \) \(\mathstrut -\mathstrut 12824497315q^{63} \) \(\mathstrut +\mathstrut 13615008977q^{64} \) \(\mathstrut -\mathstrut 2914537052q^{65} \) \(\mathstrut +\mathstrut 891867824q^{66} \) \(\mathstrut -\mathstrut 17170761380q^{67} \) \(\mathstrut +\mathstrut 36598047990q^{68} \) \(\mathstrut -\mathstrut 11808442704q^{69} \) \(\mathstrut -\mathstrut 3006503388q^{70} \) \(\mathstrut -\mathstrut 7747961400q^{71} \) \(\mathstrut -\mathstrut 7237262385q^{72} \) \(\mathstrut -\mathstrut 24853197998q^{73} \) \(\mathstrut +\mathstrut 4955041758q^{74} \) \(\mathstrut +\mathstrut 11893755908q^{75} \) \(\mathstrut +\mathstrut 11061587194q^{76} \) \(\mathstrut +\mathstrut 4844382452q^{77} \) \(\mathstrut +\mathstrut 19699573880q^{78} \) \(\mathstrut -\mathstrut 52902212480q^{79} \) \(\mathstrut -\mathstrut 25423990864q^{80} \) \(\mathstrut +\mathstrut 82069315789q^{81} \) \(\mathstrut -\mathstrut 92408290926q^{82} \) \(\mathstrut +\mathstrut 128838218460q^{83} \) \(\mathstrut +\mathstrut 51064136662q^{84} \) \(\mathstrut +\mathstrut 17293659084q^{85} \) \(\mathstrut +\mathstrut 71981969896q^{86} \) \(\mathstrut -\mathstrut 36276200504q^{87} \) \(\mathstrut +\mathstrut 79695820872q^{88} \) \(\mathstrut -\mathstrut 193189723934q^{89} \) \(\mathstrut -\mathstrut 273768252412q^{90} \) \(\mathstrut +\mathstrut 31457224918q^{91} \) \(\mathstrut -\mathstrut 269180571312q^{92} \) \(\mathstrut +\mathstrut 274848055968q^{93} \) \(\mathstrut +\mathstrut 374073101844q^{94} \) \(\mathstrut +\mathstrut 96812954440q^{95} \) \(\mathstrut -\mathstrut 460410920270q^{96} \) \(\mathstrut -\mathstrut 263465735750q^{97} \) \(\mathstrut +\mathstrut 6496930727q^{98} \) \(\mathstrut -\mathstrut 158745210908q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(7))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 7
7.12.a.a \(2\) \(5.378\) \(\Q(\sqrt{3369}) \) None \(-54\) \(120\) \(-13500\) \(33614\) \(-\) \(q+(-3^{3}-\beta )q^{2}+(60+6\beta )q^{3}+(2050+\cdots)q^{4}+\cdots\)
7.12.a.b \(3\) \(5.378\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(77\) \(-140\) \(5026\) \(-50421\) \(+\) \(q+(26+\beta _{2})q^{2}+(-47-11\beta _{1}+10\beta _{2})q^{3}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(7))\) into lower level spaces

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