# Properties

 Label 1575.2.bc Level 1575 Weight 2 Character orbit bc Rep. character $$\chi_{1575}(899,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 96 Newform subspaces 5 Sturm bound 480 Trace bound 11

# Related objects

## Defining parameters

 Level: $$N$$ = $$1575 = 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 1575.bc (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$105$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$5$$ Sturm bound: $$480$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$2$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1575, [\chi])$$.

Total New Old
Modular forms 528 96 432
Cusp forms 432 96 336
Eisenstein series 96 0 96

## Trace form

 $$96q - 48q^{4} + O(q^{10})$$ $$96q - 48q^{4} - 48q^{16} - 12q^{19} + 24q^{31} + 24q^{46} - 12q^{49} - 12q^{61} + 96q^{64} - 24q^{79} + 12q^{91} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1575, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1575.2.bc.a $$8$$ $$12.576$$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{24}^{4}+\zeta_{24}^{7})q^{2}+(3\zeta_{24}-2\zeta_{24}^{3}+\cdots)q^{7}+\cdots$$
1575.2.bc.b $$8$$ $$12.576$$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2\zeta_{24}^{2}q^{4}+(2\zeta_{24}+\zeta_{24}^{3})q^{7}-\zeta_{24}^{5}q^{11}+\cdots$$
1575.2.bc.c $$24$$ $$12.576$$ None $$0$$ $$0$$ $$0$$ $$0$$
1575.2.bc.d $$24$$ $$12.576$$ None $$0$$ $$0$$ $$0$$ $$0$$
1575.2.bc.e $$32$$ $$12.576$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1575, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1575, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(315, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(525, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ ($$( 1 - 2 T^{2} )^{4}( 1 + 2 T^{2} + 4 T^{4} )^{2}$$)($$( 1 - 2 T^{2} + 4 T^{4} )^{4}$$)
$3$ 1
$5$ 1
$7$ ($$( 1 - 13 T^{2} + 49 T^{4} )^{2}$$)($$( 1 + 2 T^{2} + 49 T^{4} )^{2}$$)
$11$ ($$( 1 + 20 T^{2} + 279 T^{4} + 2420 T^{6} + 14641 T^{8} )^{2}$$)($$( 1 + 4 T^{2} - 105 T^{4} + 484 T^{6} + 14641 T^{8} )^{2}$$)
$13$ ($$( 1 - T^{2} + 169 T^{4} )^{4}$$)($$( 1 + 14 T^{2} + 169 T^{4} )^{4}$$)
$17$ ($$( 1 + 10 T^{2} - 189 T^{4} + 2890 T^{6} + 83521 T^{8} )^{2}$$)($$( 1 - 20 T^{2} + 111 T^{4} - 5780 T^{6} + 83521 T^{8} )^{2}$$)
$19$ ($$( 1 + 3 T + 22 T^{2} + 57 T^{3} + 361 T^{4} )^{4}$$)($$( 1 + 12 T + 67 T^{2} + 228 T^{3} + 361 T^{4} )^{4}$$)
$23$ ($$( 1 - 14 T^{2} - 333 T^{4} - 7406 T^{6} + 279841 T^{8} )^{2}$$)($$( 1 + 26 T^{2} + 147 T^{4} + 13754 T^{6} + 279841 T^{8} )^{2}$$)
$29$ ($$( 1 - 50 T^{2} + 841 T^{4} )^{4}$$)($$( 1 + 14 T^{2} + 841 T^{4} )^{4}$$)
$31$ ($$( 1 - 7 T + 31 T^{2} )^{4}( 1 + 4 T + 31 T^{2} )^{4}$$)($$( 1 - 9 T + 58 T^{2} - 279 T^{3} + 961 T^{4} )^{4}$$)
$37$ ($$( 1 + 26 T^{2} + 1369 T^{4} )^{2}( 1 + 47 T^{2} + 1369 T^{4} )^{2}$$)($$( 1 + 26 T^{2} + 1369 T^{4} )^{2}( 1 + 47 T^{2} + 1369 T^{4} )^{2}$$)
$41$ ($$( 1 + 28 T^{2} + 1681 T^{4} )^{4}$$)($$( 1 + 28 T^{2} + 1681 T^{4} )^{4}$$)
$43$ ($$( 1 - 85 T^{2} + 1849 T^{4} )^{4}$$)($$( 1 - 85 T^{2} + 1849 T^{4} )^{4}$$)
$47$ ($$( 1 - 56 T^{2} + 927 T^{4} - 123704 T^{6} + 4879681 T^{8} )^{2}$$)($$( 1 + 40 T^{2} - 609 T^{4} + 88360 T^{6} + 4879681 T^{8} )^{2}$$)
$53$ ($$( 1 - 98 T^{2} + 6795 T^{4} - 275282 T^{6} + 7890481 T^{8} )^{2}$$)($$( 1 - 88 T^{2} + 4935 T^{4} - 247192 T^{6} + 7890481 T^{8} )^{2}$$)
$59$ ($$( 1 - 94 T^{2} + 5355 T^{4} - 327214 T^{6} + 12117361 T^{8} )^{2}$$)($$( 1 - 64 T^{2} + 615 T^{4} - 222784 T^{6} + 12117361 T^{8} )^{2}$$)
$61$ ($$( 1 + 6 T + 73 T^{2} + 366 T^{3} + 3721 T^{4} )^{4}$$)($$( 1 + 3 T + 64 T^{2} + 183 T^{3} + 3721 T^{4} )^{4}$$)
$67$ ($$( 1 - 109 T^{2} + 4489 T^{4} )^{2}( 1 + 122 T^{2} + 4489 T^{4} )^{2}$$)($$( 1 + 130 T^{2} + 12411 T^{4} + 583570 T^{6} + 20151121 T^{8} )^{2}$$)
$71$ ($$( 1 - 92 T^{2} + 5041 T^{4} )^{4}$$)($$( 1 - 124 T^{2} + 5041 T^{4} )^{4}$$)
$73$ ($$( 1 - 97 T^{2} + 5329 T^{4} )^{2}( 1 - 46 T^{2} + 5329 T^{4} )^{2}$$)($$( 1 - 71 T^{2} - 288 T^{4} - 378359 T^{6} + 28398241 T^{8} )^{2}$$)
$79$ ($$( 1 - 5 T - 54 T^{2} - 395 T^{3} + 6241 T^{4} )^{4}$$)($$( 1 - 4 T + 79 T^{2} )^{4}( 1 + 17 T + 79 T^{2} )^{4}$$)
$83$ ($$( 1 - 112 T^{2} + 6889 T^{4} )^{4}$$)($$( 1 - 112 T^{2} + 6889 T^{4} )^{4}$$)
$89$ ($$( 1 - 154 T^{2} + 15795 T^{4} - 1219834 T^{6} + 62742241 T^{8} )^{2}$$)($$( 1 - 124 T^{2} + 7455 T^{4} - 982204 T^{6} + 62742241 T^{8} )^{2}$$)
$97$ ($$( 1 + 86 T^{2} + 9409 T^{4} )^{4}$$)($$( 1 + 191 T^{2} + 9409 T^{4} )^{4}$$)