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Properties

Label 4.26.a
Level $4$
Weight $26$
Character orbit 4.a
Rep. character $\chi_{4}(1,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $13$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 4 = 2^{2} \)
Weight: \( k \) \(=\) \( 26 \)
Character orbit: \([\chi]\) \(=\) 4.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(13\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_0(4))\).

Total New Old
Modular forms 14 2 12
Cusp forms 11 2 9
Eisenstein series 3 0 3

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

\(2\)Dim
\(-\)\(2\)

Trace form

\( 2 q - 899640 q^{3} - 399350196 q^{5} - 40518462320 q^{7} + 848785998042 q^{9} + O(q^{10}) \) \( 2 q - 899640 q^{3} - 399350196 q^{5} - 40518462320 q^{7} + 848785998042 q^{9} - 1306289379240 q^{11} + 32729023492060 q^{13} + 1129212800709552 q^{15} + 4624697010380580 q^{17} + 24674021780774632 q^{19} + 114967389360140352 q^{21} - 31042927879759440 q^{23} - 94693927809381634 q^{25} - 1543594702580385840 q^{27} - 3328137384414404868 q^{29} - 6421803981270308288 q^{31} + 9385715601558142560 q^{33} + 51043698274430238048 q^{35} + 31687565809212923020 q^{37} + 49526653229543938032 q^{39} - 16316808963958618668 q^{41} - 341165113066738242920 q^{43} - 1023758965576016818596 q^{45} - 1118172622498866698400 q^{47} + 2514734995497417690354 q^{49} + 774064747141339317264 q^{51} + 7614510009160367483820 q^{53} + 4167198967582958322960 q^{55} - 4468294635852504762720 q^{57} - 4439075167218253907016 q^{59} - 10634755765830886628036 q^{61} - 104228162020256173326000 q^{63} + 21991306250852228329128 q^{65} - 27985598617668512548280 q^{67} + 308855371847014830833856 q^{69} - 31606985976821340133104 q^{71} + 390343645433421883811860 q^{73} - 336618576615723339381192 q^{75} + 424438601780393611266240 q^{77} - 1143923903407761106308704 q^{79} - 63792847020367292545422 q^{81} - 2544503743336324024143000 q^{83} + 343892775851675596114776 q^{85} + 579335111505652549849200 q^{87} + 3902025208165068648348468 q^{89} + 2243166387869650274782688 q^{91} + 9713299019180457972015360 q^{93} - 1982812931470769310151056 q^{95} - 8231826212771633749326140 q^{97} - 8469521205549833375650440 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_0(4))\) 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
4.26.a.a 4.a 1.a $2$ $15.840$ \(\Q(\sqrt{358121}) \) None \(0\) \(-899640\) \(-399350196\) \(-40518462320\) $-$ $\mathrm{SU}(2)$ \(q+(-449820-\beta )q^{3}+(-199675098+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{26}^{\mathrm{old}}(\Gamma_0(4))\) into lower level spaces

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