# Properties

 Label 26.6.a Level $26$ Weight $6$ Character orbit 26.a Rep. character $\chi_{26}(1,\cdot)$ Character field $\Q$ Dimension $5$ Newform subspaces $3$ Sturm bound $21$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$26 = 2 \cdot 13$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 26.a (trivial) Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$21$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(\Gamma_0(26))$$.

Total New Old
Modular forms 19 5 14
Cusp forms 15 5 10
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.

$$2$$$$13$$FrickeDim
$$+$$$$+$$$$+$$$$1$$
$$+$$$$-$$$$-$$$$2$$
$$-$$$$+$$$$-$$$$2$$
Plus space$$+$$$$1$$
Minus space$$-$$$$4$$

## Trace form

 $$5 q - 4 q^{2} + 18 q^{3} + 80 q^{4} + 22 q^{5} + 312 q^{7} - 64 q^{8} + 683 q^{9} + O(q^{10})$$ $$5 q - 4 q^{2} + 18 q^{3} + 80 q^{4} + 22 q^{5} + 312 q^{7} - 64 q^{8} + 683 q^{9} + 496 q^{10} - 384 q^{11} + 288 q^{12} - 169 q^{13} - 8 q^{14} - 2504 q^{15} + 1280 q^{16} + 392 q^{17} - 2900 q^{18} - 1332 q^{19} + 352 q^{20} - 3044 q^{21} - 224 q^{22} - 4156 q^{23} - 6867 q^{25} - 2028 q^{26} + 16146 q^{27} + 4992 q^{28} + 6122 q^{29} + 2456 q^{30} - 6368 q^{31} - 1024 q^{32} - 4340 q^{33} - 3080 q^{34} + 14842 q^{35} + 10928 q^{36} + 42102 q^{37} - 14640 q^{38} + 7936 q^{40} + 734 q^{41} - 12808 q^{42} + 5526 q^{43} - 6144 q^{44} - 38878 q^{45} - 7728 q^{46} - 64560 q^{47} + 4608 q^{48} + 46119 q^{49} + 29348 q^{50} - 42458 q^{51} - 2704 q^{52} + 13646 q^{53} - 52272 q^{54} - 22760 q^{55} - 128 q^{56} - 77648 q^{57} - 9288 q^{58} - 32292 q^{59} - 40064 q^{60} + 63642 q^{61} + 47856 q^{62} + 147600 q^{63} + 20480 q^{64} - 16224 q^{65} + 90944 q^{66} + 41680 q^{67} + 6272 q^{68} - 46788 q^{69} + 77584 q^{70} - 14176 q^{71} - 46400 q^{72} + 50422 q^{73} - 25968 q^{74} - 59164 q^{75} - 21312 q^{76} - 38256 q^{77} - 12168 q^{78} + 112708 q^{79} + 5632 q^{80} + 193637 q^{81} + 90136 q^{82} - 202896 q^{83} - 48704 q^{84} + 136096 q^{85} - 54656 q^{86} - 206184 q^{87} - 3584 q^{88} + 28670 q^{89} + 57688 q^{90} + 57798 q^{91} - 66496 q^{92} - 263712 q^{93} + 54328 q^{94} - 91924 q^{95} + 136986 q^{97} - 82212 q^{98} + 70148 q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(\Gamma_0(26))$$ into newform subspaces

Label Dim $A$ Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 13
26.6.a.a $1$ $4.170$ $$\Q$$ None $$-4$$ $$0$$ $$-14$$ $$-170$$ $+$ $+$ $$q-4q^{2}+2^{4}q^{4}-14q^{5}-170q^{7}+\cdots$$
26.6.a.b $2$ $4.170$ $$\Q(\sqrt{2785})$$ None $$-8$$ $$9$$ $$-37$$ $$327$$ $+$ $-$ $$q-4q^{2}+(5-\beta )q^{3}+2^{4}q^{4}+(-19+\cdots)q^{5}+\cdots$$
26.6.a.c $2$ $4.170$ $$\Q(\sqrt{849})$$ None $$8$$ $$9$$ $$73$$ $$155$$ $-$ $+$ $$q+4q^{2}+(5-\beta )q^{3}+2^{4}q^{4}+(35+3\beta )q^{5}+\cdots$$

## Decomposition of $$S_{6}^{\mathrm{old}}(\Gamma_0(26))$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(\Gamma_0(26)) \simeq$$ $$S_{6}^{\mathrm{new}}(\Gamma_0(13))$$$$^{\oplus 2}$$