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Properties

Label 12.26.a
Level $12$
Weight $26$
Character orbit 12.a
Rep. character $\chi_{12}(1,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $52$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) \(=\) \( 26 \)
Character orbit: \([\chi]\) \(=\) 12.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(52\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_0(12))\).

Total New Old
Modular forms 53 4 49
Cusp forms 47 4 43
Eisenstein series 6 0 6

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

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

Trace form

\( 4 q + 698992200 q^{5} + 26447813840 q^{7} + 1129718145924 q^{9} + O(q^{10}) \) \( 4 q + 698992200 q^{5} + 26447813840 q^{7} + 1129718145924 q^{9} - 15289321059936 q^{11} - 133850996468200 q^{13} + 160426519822800 q^{15} - 3106911674542680 q^{17} - 27888100379874400 q^{19} - 39578862692541744 q^{21} - 79613267278001760 q^{23} + 414419890179917500 q^{25} + 3815362555448382216 q^{29} + 4716563232169269776 q^{31} - 6266215808542427760 q^{33} - 59172886962247168800 q^{35} + 27287752296790621400 q^{37} - 35009652822990300000 q^{39} + 59590607636871036360 q^{41} + 93558154042521402080 q^{43} + 197416043049834448200 q^{45} + 1396293369956222565600 q^{47} - 736156114320190622364 q^{49} + 100099152144963750816 q^{51} - 7050951549782064567000 q^{53} - 9323522639951680828800 q^{55} + 1574336559721907755440 q^{57} + 23531292848518366663296 q^{59} + 35221832538614604395768 q^{61} + 7469643803766976697040 q^{63} - 58692654968402279106000 q^{65} + 71834764529825361019520 q^{67} - 130299358109856273013824 q^{69} + 79910318376833930042400 q^{71} - 480391356101638942805080 q^{73} + 248524047150727557960000 q^{75} - 304357868832149139585600 q^{77} + 857992130927027719018832 q^{79} + 319065772307490039453444 q^{81} + 1836624673242913166123040 q^{83} - 884792423259964111546800 q^{85} - 846589065980090836456080 q^{87} - 2541407900736287098526040 q^{89} - 2412124225976825940912800 q^{91} - 1014760313096966010274320 q^{93} - 495724501863513512928000 q^{95} + 5332674117583972268294600 q^{97} - 4318155860066916099525216 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_0(12))\) 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 3
12.26.a.a 12.a 1.a $2$ $47.520$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(0\) \(-1062882\) \(198560700\) \(50461213312\) $-$ $+$ $\mathrm{SU}(2)$ \(q-3^{12}q^{3}+(99280350-\beta )q^{5}+(25230606656+\cdots)q^{7}+\cdots\)
12.26.a.b 12.a 1.a $2$ $47.520$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(0\) \(1062882\) \(500431500\) \(-24013399472\) $-$ $-$ $\mathrm{SU}(2)$ \(q+3^{12}q^{3}+(250215750-5\beta )q^{5}+\cdots\)

Decomposition of \(S_{26}^{\mathrm{old}}(\Gamma_0(12))\) into lower level spaces

\( S_{26}^{\mathrm{old}}(\Gamma_0(12)) \cong \) \(S_{26}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)