# Properties

 Label 12.28.a Level $12$ Weight $28$ Character orbit 12.a Rep. character $\chi_{12}(1,\cdot)$ Character field $\Q$ Dimension $5$ Newform subspaces $2$ Sturm bound $56$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$12 = 2^{2} \cdot 3$$ Weight: $$k$$ $$=$$ $$28$$ Character orbit: $$[\chi]$$ $$=$$ 12.a (trivial) Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$56$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{28}(\Gamma_0(12))$$.

Total New Old
Modular forms 57 5 52
Cusp forms 51 5 46
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
$$-$$$$+$$$$-$$$$2$$
$$-$$$$-$$$$+$$$$3$$
Plus space$$+$$$$3$$
Minus space$$-$$$$2$$

## Trace form

 $$5 q + 1594323 q^{3} - 963806058 q^{5} + 79029905368 q^{7} + 12709329141645 q^{9} + O(q^{10})$$ $$5 q + 1594323 q^{3} - 963806058 q^{5} + 79029905368 q^{7} + 12709329141645 q^{9} + 33733959495300 q^{11} + 670276799043790 q^{13} + 3256284678166746 q^{15} + 52052252916873978 q^{17} + 374647792087464700 q^{19} + 532749624506155080 q^{21} + 7098202550496408552 q^{23} + 17586452464619891459 q^{25} + 4052555153018976267 q^{27} - 100100215522540863810 q^{29} - 279846729146092941440 q^{31} - 167504371596450661572 q^{33} - 533783946802147362864 q^{35} + 1470879265979922168694 q^{37} + 585456075276279785730 q^{39} + 11061235667172640154850 q^{41} + 17827080101783737880932 q^{43} - 2449865683966678217082 q^{45} - 31680092500634433215088 q^{47} - 93840947959150198314675 q^{49} - 14201865684590851099530 q^{51} - 26171143951591950140826 q^{53} + 392836601680540163118072 q^{55} + 394558724697986766059460 q^{57} + 2237484144411917263905300 q^{59} + 2686412671576531413719710 q^{61} + 200883415870993803570072 q^{63} + 1501835229060419387637540 q^{65} - 5966841675545340699034868 q^{67} + 38569005320782629009240 q^{69} - 8571270448497844102388040 q^{71} + 37548078331156987525436866 q^{73} + 3071267103553605729984357 q^{75} + 94509136054084009442910048 q^{77} + 12816848456319977307662800 q^{79} + 32305409446133366494661205 q^{81} - 143621211653693586763173828 q^{83} + 8701094885997936762475596 q^{85} - 109065743206428551751323982 q^{87} - 28117383175530694790303310 q^{89} - 874133563771099870943563120 q^{91} + 19617607716418167772000032 q^{93} - 797863993520564514609559800 q^{95} + 1039895871024579183513286186 q^{97} + 85747198895337669282353700 q^{99} + O(q^{100})$$

## Decomposition of $$S_{28}^{\mathrm{new}}(\Gamma_0(12))$$ into newform subspaces

Label Dim $A$ Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3
12.28.a.a $2$ $55.423$ $$\mathbb{Q}[x]/(x^{2} - \cdots)$$ None $$0$$ $$-3188646$$ $$-1503115380$$ $$-127562115296$$ $-$ $+$ $$q-3^{13}q^{3}+(-751557690-11\beta )q^{5}+\cdots$$
12.28.a.b $3$ $55.423$ $$\mathbb{Q}[x]/(x^{3} - \cdots)$$ None $$0$$ $$4782969$$ $$539309322$$ $$206592020664$$ $-$ $-$ $$q+3^{13}q^{3}+(179769774-\beta _{1})q^{5}+\cdots$$

## Decomposition of $$S_{28}^{\mathrm{old}}(\Gamma_0(12))$$ into lower level spaces

$$S_{28}^{\mathrm{old}}(\Gamma_0(12)) \simeq$$ $$S_{28}^{\mathrm{new}}(\Gamma_0(1))$$$$^{\oplus 6}$$$$\oplus$$$$S_{28}^{\mathrm{new}}(\Gamma_0(2))$$$$^{\oplus 4}$$$$\oplus$$$$S_{28}^{\mathrm{new}}(\Gamma_0(3))$$$$^{\oplus 3}$$$$\oplus$$$$S_{28}^{\mathrm{new}}(\Gamma_0(4))$$$$^{\oplus 2}$$$$\oplus$$$$S_{28}^{\mathrm{new}}(\Gamma_0(6))$$$$^{\oplus 2}$$