# Properties

 Label 26.4.a Level $26$ Weight $4$ Character orbit 26.a Rep. character $\chi_{26}(1,\cdot)$ Character field $\Q$ Dimension $3$ Newform subspaces $3$ Sturm bound $14$ Trace bound $3$

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## Defining parameters

 Level: $$N$$ $$=$$ $$26 = 2 \cdot 13$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 26.a (trivial) Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$14$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

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

Total New Old
Modular forms 13 3 10
Cusp forms 9 3 6
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
$$+$$$$+$$$$+$$$$1$$
$$-$$$$-$$$$+$$$$2$$
Plus space$$+$$$$3$$
Minus space$$-$$$$0$$

## Trace form

 $$3 q + 2 q^{2} + 6 q^{3} + 12 q^{4} + 10 q^{5} + 4 q^{7} + 8 q^{8} - 55 q^{9} + O(q^{10})$$ $$3 q + 2 q^{2} + 6 q^{3} + 12 q^{4} + 10 q^{5} + 4 q^{7} + 8 q^{8} - 55 q^{9} - 24 q^{10} - 84 q^{11} + 24 q^{12} + 13 q^{13} - 68 q^{14} - 56 q^{15} + 48 q^{16} - 4 q^{17} - 38 q^{18} + 168 q^{19} + 40 q^{20} + 172 q^{21} - 16 q^{22} + 44 q^{23} + 359 q^{25} + 78 q^{26} - 234 q^{27} + 16 q^{28} + 62 q^{29} - 244 q^{30} + 212 q^{31} + 32 q^{32} - 308 q^{33} + 196 q^{34} - 746 q^{35} - 220 q^{36} - 198 q^{37} - 24 q^{38} - 96 q^{40} - 358 q^{41} + 116 q^{42} + 490 q^{43} - 336 q^{44} - 442 q^{45} + 296 q^{46} - 372 q^{47} + 96 q^{48} + 957 q^{49} + 734 q^{50} + 130 q^{51} + 52 q^{52} + 794 q^{53} + 72 q^{54} + 480 q^{55} - 272 q^{56} + 112 q^{57} + 884 q^{58} + 48 q^{59} - 224 q^{60} - 170 q^{61} - 744 q^{62} + 348 q^{63} + 192 q^{64} - 156 q^{65} - 160 q^{66} - 1036 q^{67} - 16 q^{68} + 588 q^{69} - 2328 q^{70} - 1228 q^{71} - 152 q^{72} - 798 q^{73} + 1368 q^{74} + 620 q^{75} + 672 q^{76} - 1752 q^{77} + 156 q^{78} + 1332 q^{79} + 160 q^{80} + 419 q^{81} - 1964 q^{82} + 948 q^{83} + 688 q^{84} - 2072 q^{85} - 512 q^{86} - 792 q^{87} - 64 q^{88} + 1562 q^{89} - 92 q^{90} - 442 q^{91} + 176 q^{92} + 1056 q^{93} - 580 q^{94} + 2876 q^{95} - 2794 q^{97} + 1842 q^{98} + 1160 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_0(26))$$ into newform subspaces

Label Dim $A$ Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 13
26.4.a.a $1$ $1.534$ $$\Q$$ None $$-2$$ $$3$$ $$11$$ $$19$$ $+$ $+$ $$q-2q^{2}+3q^{3}+4q^{4}+11q^{5}-6q^{6}+\cdots$$
26.4.a.b $1$ $1.534$ $$\Q$$ None $$2$$ $$-1$$ $$17$$ $$-35$$ $-$ $-$ $$q+2q^{2}-q^{3}+4q^{4}+17q^{5}-2q^{6}+\cdots$$
26.4.a.c $1$ $1.534$ $$\Q$$ None $$2$$ $$4$$ $$-18$$ $$20$$ $-$ $-$ $$q+2q^{2}+4q^{3}+4q^{4}-18q^{5}+8q^{6}+\cdots$$

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

$$S_{4}^{\mathrm{old}}(\Gamma_0(26)) \simeq$$ $$S_{4}^{\mathrm{new}}(\Gamma_0(13))$$$$^{\oplus 2}$$