# Properties

 Label 12.4.a Level $12$ Weight $4$ Character orbit 12.a Rep. character $\chi_{12}(1,\cdot)$ Character field $\Q$ Dimension $1$ Newform subspaces $1$ Sturm bound $8$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$12 = 2^{2} \cdot 3$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 12.a (trivial) Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$8$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_0(12))$$.

Total New Old
Modular forms 9 1 8
Cusp forms 3 1 2
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.
$$-$$$$-$$$$+$$$$1$$
Plus space$$+$$$$1$$
Minus space$$-$$$$0$$

## Trace form

 $$q + 3q^{3} - 18q^{5} + 8q^{7} + 9q^{9} + O(q^{10})$$ $$q + 3q^{3} - 18q^{5} + 8q^{7} + 9q^{9} + 36q^{11} - 10q^{13} - 54q^{15} + 18q^{17} - 100q^{19} + 24q^{21} + 72q^{23} + 199q^{25} + 27q^{27} - 234q^{29} - 16q^{31} + 108q^{33} - 144q^{35} - 226q^{37} - 30q^{39} + 90q^{41} + 452q^{43} - 162q^{45} + 432q^{47} - 279q^{49} + 54q^{51} + 414q^{53} - 648q^{55} - 300q^{57} - 684q^{59} + 422q^{61} + 72q^{63} + 180q^{65} + 332q^{67} + 216q^{69} - 360q^{71} + 26q^{73} + 597q^{75} + 288q^{77} + 512q^{79} + 81q^{81} - 1188q^{83} - 324q^{85} - 702q^{87} - 630q^{89} - 80q^{91} - 48q^{93} + 1800q^{95} - 1054q^{97} + 324q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_0(12))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 2 3
12.4.a.a $$1$$ $$0.708$$ $$\Q$$ None $$0$$ $$3$$ $$-18$$ $$8$$ $$-$$ $$-$$ $$q+3q^{3}-18q^{5}+8q^{7}+9q^{9}+6^{2}q^{11}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_0(12))$$ into lower level spaces

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