Properties

Label 29.12.a
Level $29$
Weight $12$
Character orbit 29.a
Rep. character $\chi_{29}(1,\cdot)$
Character field $\Q$
Dimension $25$
Newform subspaces $2$
Sturm bound $30$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 29.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(30\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(29))\).

Total New Old
Modular forms 29 25 4
Cusp forms 27 25 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 and the Fricke involution.

\(29\)Dim.
\(+\)\(14\)
\(-\)\(11\)

Trace form

\( 25q - 32q^{2} - 506q^{3} + 27508q^{4} + 7020q^{5} - 9748q^{6} + 35592q^{7} - 23466q^{8} + 1702895q^{9} + O(q^{10}) \) \( 25q - 32q^{2} - 506q^{3} + 27508q^{4} + 7020q^{5} - 9748q^{6} + 35592q^{7} - 23466q^{8} + 1702895q^{9} + 27742q^{10} - 214226q^{11} - 1448262q^{12} + 3782804q^{13} - 3244312q^{14} - 7226682q^{15} + 22039956q^{16} + 2332410q^{17} - 28089770q^{18} - 14318088q^{19} + 15688344q^{20} + 4311032q^{21} + 123898648q^{22} - 36029772q^{23} - 3185836q^{24} + 150774941q^{25} + 48581774q^{26} + 161043970q^{27} - 71773076q^{28} - 61533447q^{29} - 71896156q^{30} + 341805414q^{31} + 627748370q^{32} + 101067010q^{33} + 202797124q^{34} + 287033648q^{35} + 961349640q^{36} - 891764134q^{37} + 669987788q^{38} + 785688014q^{39} - 886667226q^{40} - 863852330q^{41} + 1216983428q^{42} + 2267776694q^{43} + 79414186q^{44} + 3398674874q^{45} - 1655195592q^{46} - 5997173870q^{47} - 12916902578q^{48} + 5797744465q^{49} + 2863677314q^{50} + 12065621100q^{51} - 1290671508q^{52} - 5404446152q^{53} + 8456593504q^{54} - 2917362106q^{55} - 16274680360q^{56} - 8981654972q^{57} - 656356768q^{58} + 1582222352q^{59} - 4208701494q^{60} - 26261200706q^{61} + 12051817568q^{62} - 33002113192q^{63} + 26534985848q^{64} + 33398592218q^{65} - 56828053010q^{66} + 49262818932q^{67} - 74589188368q^{68} - 35166714476q^{69} - 25086206272q^{70} - 25920455684q^{71} + 22998940072q^{72} - 18078498554q^{73} + 25865342492q^{74} + 58300418044q^{75} + 133599439548q^{76} + 39645526984q^{77} + 38864633664q^{78} - 14679807442q^{79} + 61922455276q^{80} + 121701036885q^{81} - 64150349656q^{82} - 14617919800q^{83} + 81165635120q^{84} - 97745332000q^{85} - 55291873840q^{86} - 29905255242q^{87} + 237645067640q^{88} + 91125382134q^{89} + 70813178716q^{90} - 296771641312q^{91} - 282075353192q^{92} + 222059520878q^{93} + 290303285012q^{94} - 125987091284q^{95} + 238924679544q^{96} - 165904914514q^{97} - 608672866304q^{98} + 96294484764q^{99} + O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(29))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 29
29.12.a.a \(11\) \(22.282\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-32\) \(-982\) \(-2740\) \(-49432\) \(-\) \(q+(-3+\beta _{1})q^{2}+(-89-\beta _{1}-\beta _{3}+\cdots)q^{3}+\cdots\)
29.12.a.b \(14\) \(22.282\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(476\) \(9760\) \(85024\) \(+\) \(q+\beta _{1}q^{2}+(34-\beta _{3})q^{3}+(1312+3\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(29))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(29)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)